THE  PRATT  &  WHITNEY  Co, 


STANDARDS  OF  LENGTH 


AND   THEIR 


PRACTICAL  APPLICATION. 


A    RESUME    COVERING    THE    METHODS    EMPLOYED    FOR    THE    PRO- 
DUCTION   OF    STANDARD    GAUGES. 

TO    INSURE 

UNIFORMITY   AND    INTERCHANGEABILITY   IN   EVERY 
DEPARTMENT   OF    MANUFACTURES, 

INCLUDING 

THE    REPORTS 

OF 

PROFESSOR    WM.    A.    ROGERS;     THE    COMMITTEE    ON    STANDARDS    AND    GAUGES, 
AMERICAN     SOCIETY    OF    MECHANICAL     ENGINEERS;     THE    COMMITTEE 
OF    THE    MASTER   CAR-BUILDERS'    ASSOCIATION;     AND   INCLUD- 
ING  ALSO   THE  REPORT  OF   THE   SPECIAL  COMMITTEE 
APPOINTED    BY    THE    FRANKLIN    INSTITUTE, 
APRIL,    1864. 


Edited   by   GEORGE    M.  BOND,  M.E. 


PUBLISHED    BY 

THE  PRATT  &   ^S^osiTiisrE 

Hartford,   Conn.,    U.  S.  A. 

1887. 


THE  CASE,  LOCKWOOD  &  BRAINARD  Co.,  PRINTERS,  HARTFORD.  CON* 


QC 


niO  OUR  FRIENDS,  wrp  r]ave  given  us  trjeir  eqcouragerqent  during 
trje  progress  of  th[e  work  of  establishing  a  staqdard  for  gauge 
dimensions,  aqd  to  all  wr|O  appreciate  tP|e  advantages  resulting  frorq 
practical  uqifornr|ity  iq  lesseqing  tf]e  cost  of  maqufactures,  this  col- 
lectioq  of  reports  aqd  data  is  respectfully  dedicated  by 

THE  PRATT  &  WHITNEY  COMPANY. 


M323716 


EEPOKT  OF  PEOFESSOE  WM.  A.  EOGEES. 


THE  PRATT  &  WHITNEY  Co., 

Gentlemen:- — I  communicate  herewith  the  results  of  my 
investigation  of  the  units  of  length  upon  which  your  system  of 
gauges  depends. 

In  the  preliminary  discussion  of  this  question  with  you,  cer- 
tain considerations  were  urged  by  which  we  should  be  governed 
in  the  construction  and  adoption  of  standards  of  length  for  prac- 
tical use  in  mechanical  operations.  In  iny  letter  of  May  26, 
1880,  these  were  enumerated  as  follows : 

First.  For  ,the  yard  as  a  standard  unit,  the  material  employed 
should  be  an  alloy  known  as  Baily's  metal,  composed  of  16 
parts  of  copper,  2J  parts  of  tin,  and  1  part  of  zinc,  since  this  is 
the  composition  of  the  Imperial  Yard  of  Great  Britain,  to  which 
final  reference  will  be  made,  and  of  the  standard  yard,  "  Bronze 
11 "  of  the  United  States  Bureau  of  Weights  and  Measures. 

Second.  The  particular  standard  yard  or  yards  constructed 
should  be  referred  to  one  of  the  two  yards  named,  and  not  to 
any  copy  in  the  hands  of  a  private  person.  This  standard  of 
reference  ought  to  be  within  easy  access,  in  order  that  compari- 
sons with  it  may  be  made  at  stated  intervals  for  the  purpose  of 
ascertaining  whether  a  constant  relation  between  the  two  units 
is  maintained.  Since  the  latter  consideration  would  prevent  a 
direct  reference  to  the  Imperial  Yard  No.  1,  I  strongly  urge 
the  importance  of  referring  the  proposed  standard  yard,  which 
you  have  empowered  me  to  construct,  directly  to  "  Bronze  11." 
This  standard  is  not  a  legal  standard  in  the  sense  that  it  has  been 
authorized  as  such  by  an  act  of  Congress,  but  since  it  has  been 
in  actual  use  for  many  years,  and  since  it  will,  without  doubt, 
receive  a  legal  authorization  in  the  near  future,  this  objection 
has  but  little  practical  force. 

By  the  adoption  of  "Bronze  11,"  as  the  direct  standard  of 
reference,  the  ultimate  reference  to  the  Imperial  Yard  will  be 
secured,  since  the  relation  between  these  standards  has  already 


been  tlie  subject  of  four  distinct  investigations.  When  "Bronze 
11 "  was  presented  to  the  United  States  in  1856,  it  was  stated  to 
be  standard  at  61°.79  Fahr.  It  was,  therefore,  about  one  seven - 
thousandth  of  an  inch  too  long.  This  relation  was  the  result  of 
the  comparisons  made  at  the  time  the  standards  were  constructed. 
Two  subsequent  investigations  of  this  relation  have  been  made 
by  Professor  Ililgard  and  Mr.  Chaney,  the  Warden  of  the  Im- 
perial Standards,  giving  substantially  identical  results ;  and  for 
many  years  it  has  been  assumed  that  "Bronze  11"  is  88  mil- 
lion ths  of  an  inch  shorter  than  the  Imperial  Yard  at  62°  Fahr. 
An  investigation  by  Mr.  Charles  S.  Peirce,  however,  made  in 
1883,  reduces  this  relation  to  22  millionths  of  an  inch.  Whether 
this  apparent  variation  in  length  is  real,  will  doubtless  be  de- 
termined by  future  investigations,  but  the  deviation  will  not  be 
of  any  practical  account  within  the  limits  which  you  require  in 
your  system  of  gauges.  Admitting  a  doubt  in  the  value  of  the 
relation  as  great  as  one  ten-thousandth  of  an  inch,  the  propor- 
tional part  for  six  inches  would  be  only  one  sixty-thousandth  of 
an  inch. 

Third.  Since  your  gauges  are  made  of  tempered  steel  it  will 
be  necessary  to  construct  one  standard  of  this  material  in  order 
that  a  direct  comparison  of  the  gauges  with  the  standard  may  be 
made  without  regard  to  the  question  of  temperature. 

Fourth.  Since  there  are  no  reliable  observations  which  deter- 
mine the  behavior  of  tempered  steel  under  variations  of  tempera- 
ture when  compared  with  the  same  metal  untempered,  it  will  be 
necessary  to  have  a  standard  yard  upon  annealed  steel. 

Fifth.  On  account  of  the  difficulty  of  maintaining  a  plane 
surface  upon  a  bar  of  the  dimensions  described,  it  will  be  advisa- 
ble to  construct  a  short  standard  for  ordinary  use  in  the  con- 
struction and  comparison  of  your  gauges,  in  which  the  warping 
of  the  graduated  surface  by  flexure  may  be  neglected.  Since 
this  line  standard  will  be  the  real  basis  upon  which  your  system 
of  gauges  rests,  the  subdivisions  of  the  total  length  should  be 
such  that  any  fractional  part  thereof  may  be  readily  and  easily 
obtained. 

In  the  machine-shop  practice  of  this  country,  there  is  not,  at 
the  present  time,  any  extensive  demand  for  units  of  length 
expressed  in  the  metric  system.  Since,  however,  this  system  is 


3 

largely  adopted  in  scientific  investigations,  it  will  be  desirable  to 
construct  a  standard  meter  and  to  obtain  the  correct  subdivisions 
of  the  same.  In  order  to  avoid  the  confusion  resulting  from  the 
fact  that  the  Imperial  Yard  is  standard  at  62°  Fahr.,  and  that 
the  meter  is  standard  at  0°  Centigrade,  the  metric  unit  should  be 
traced  upon  the  same  metal  as  the  yard.  If  we  could  neglect 
this  requirement,  the  bar  for  the  meter  should  properly  be  of 
platinum,  and  it  should  have  the  same  form  and  dimensions  as 
the  Metre  des  Archives,  the  legal  standard  of  France,  and  now 
adopted  as  the  basis  of  the  prototypes  constructed  for  the  Inter- 
national Bureau  of  Weights  and  Measures.  The  great  cost  of 
platinum  would  preclude  the  use  of  this  metal,  and  the  same  con- 
sideration would  prevent  the  use  of  platinum-indium,  the  alloy 
of  which  the  prototypes  are  made.  Since,  however,  the  Inter- 
national Bureau  has  every  appliance  for  comparing  standards  of 
different  material  at  any  temperature  required,  it  does  not  seem 
necessary  to  limit  the  standard  meter  to  any  particular  material 
or  dimensions.  Therefore,  as  the  yard  and  the  meter  will  be 
represented  upon  the  same  bar,  there  is  no  reason  why  they 
should  not  be  standard  at  the  same  temperature.  The  tempera- 
ture adopted  will  be  62°. 0  Fahrenheit. 

The  fulfillment  of  the  requirements  stated  above  involves  the 
following  operations : 

(a)  The  direct  comparison  of  the  yard  upon  the  bronze  bars 
with  "Bronze  11,"  and  with  the  Imperial  Yard  indirectly, 
through  the  medium  of  the  standards  which  have  been  compared 
with  it.  These  standards  are,  a  steel  yard  belonging  to  the 
writer  which  was  compared  with  the  Imperial  Yard  in  January, 
1880,  by  Mr.  Chaney  the  Warden  of  the  Standards;  a  combined 
line-measure  yard,  and  line-measure  meter  upon  brass,  and  an 
end-measure  yard  belonging  to  the  Stevens  Institute,  kindly 
loaned  to  the  writer  by  President  Morton,  both  of  which  were 
also  compared  with  the  Imperial  Yard  by  Mr.  Chaney. 

As  a  further  check,  the  comparison  will  be  made  with  an  end- 
measure  steel  yard,  purchased  by  the  writer  of  Sir  Joseph  Whit- 
worth  &  Co.  It  was  supposed  to  be  standard  at  62°  Fahr., 
although  no  statement  to  this  effect  by  the  maker  has  been 
received. 

For  the  meter,  the  comparisons  will  be  made  with  a  meter 


upon  a  copper  bar  of  the  form  adopted  by  the  International 
Bureau  of  Weights  and  Measures.  This  bar  was  traced  for  the 
writer  from  the  working  meter  of  the  Conservatoire  des  Arts  et 
Metiers,  by  M.  Tresca,  at  2  o'clock  on  the  morning  of  February 
6,  1880.  It  is  signed  by  M.  Tresca,  by  his  son  G-.  Tresca, 
who  executed  the  transfer,  and,  at  the  request  of  M.  Tresca,  by 
myself  also,  since  I  made  one  of  the  series  of  comparisons  with 
the  original,  after  the  transfer.  From  the  official  report  of 
M.  Tresca  it  appears  that  this  meter  is  118.9  mikrons  longer 
than  the  Metre  des  Archives  at  13°. 7  Centigrade,  a  mikron  being 
equal  to  s^bo-  inch,  or  ordinarily,  with  sufficient  exactness,,  030  do- 
inch. 

The  meter  will  also  be  compared  with  the  meter  upon  brass 
belonging  to  the  Stevens  Institute,  which  has  been  compared 
directly  with  the  Prototype  of  the  International  Bureau  of 
Weights  and  Measures. 

A  further  comparison  will  be  made  with  an  end-measure  meter 
of  steel,  purchased  by  the  writer  of  the  celebrated  mechanician, 
M.  Froment  of  Paris,  and  declared  to  be  8.43  mikrons  longer 
than  the  Metre  des  Archives  at  0°  Centigrade. 

(b)  In  order  to  make  these  comparisons,  it  will  be  necessary 
to  determine  with  the  greatest  care  the  amount  of  the  change 
in  length  of  each  standard  thus  compared  for  each  degree  of 
temperature.     This  quantity  is  usually  designated  the  coefficient 
of  expansion.     It  varies  according  to  the  metal  employed. 

(c)  Having  the  standard  line-measure  yard  and  line-measure 
meter  with  their  subdivisions  traced  upon  the  same  bar,  it  will 
be  necessary  to  ascertain  the  relative  errors  of  these  subdivisions 
with  the  utmost  precision.     Then,  applying  the  proper  correc- 
tions for  these  relative  errors  to  the  proportional  error  of  the 
total  length,  we  shall  have  the  absolute  correction  for  any  sub- 
division thus  investigated  at  the  adopted  temperature. 

(d)  A  similar  investigation  must  be  made  of  the  correction 
for  total  length  and  for  errors  of  subdivision  of  the  short  steel 
line-measure  referred  to  under  division  five.     This  comparison 
may  be  made  with  any  selected  subdivision  of  the  same  length 
upon  the  different  standard  yards. 


DESCRIPTION    OF    COMPARATORS. 

For  a  description  of  the  two  comparators  with  which  this 
investigation  was  made,  the  reader  is  referred  to  a  paper  by  the 
writer  entitled  "  Studies  in  Metrology,"  published  in  the  Pro- 
ceedings of  the  American  Academy  of  Arts  and  Sciences,  vol. 
xxiii,  p.  287,  et  seq. 

DESCRIPTION    OF    STANDARD    BARS. 

The  four  bars  prepared  for  end  and  line-measure  standards  are 
described  as  follows  : 

P.  &  W.j  has  the  same  composition,  form,  and  dimensions  as 
P.  &  W.2  Polished  gold  plugs  are  inserted  at  the  bottom  of 
wells  sunk  in  the  bar  to  the  depth  of  half  an  inch  at  intervals  of 
12  inches. 

P.  &  W.2  is  a  bar  of  cast  bronze  41  inches  long,  1  inch  wide, 
and  1  inch  deep.  It  is  composed  of  16  parts  of  copper,  2£  parts 
of  tin,  and  1  part  of  zinc.  Platinum-indium  plugs,  TV  of  an 
inch  in  diameter,  are  inserted  flush  with  the  surface  at  the  points 
indicated  in  Fig.  1. 


FIG.  1. 

P.  &  W.3  is  a  bar  of  tempered  steel  40  inches  long,  1^  inches 
deep,  and  f  of  an  inch  wide.  This  bar  is  designed  both  for  line- 
measure  and  end-measure  standards.  The  shape  is  shown  in 
Fig.  2. 


r- 


FIG.  2. 

The  upper  surface  is  polished  for  receiving  the  graduations. 

P.  &  W.4  is  an  annealed  bar  of  steel.  It  has  the  same  form 
and  nearly  the  same  dimensions  as  P.  &  "W3.  Instead  of  a  plane 
surface,  however,  tempered  steel  plugs  are  inserted  at  points  cor- 
responding to  those  in  P.  &  W.3  and  five  decimeter  plugs  are 
inserted  in  the  second  half  meter. 


6 

P.  &  W.5  is  a  tempered  steel  bar  6  inches  long,  and  -J  inch  in 
cross  section.  The  space  of  4  inches  is  laid  off  upon  this  bar, 
with  subdivisions  which  will  be  hereafter  described  (page  43). 

It  gives  me  pleasure  to  say  that  these  bars  came  from  your 
establishment  in  admirable  condition  for  receiving  the  gradua- 
tions. The  surfaces  of  P.  &  WM  and  of  P.  &  W.2  were  found 
to  be  practically  parallel.  The  depth  of  the  bars  is  so  nearly  the 
same,  that  one  can  be  substituted  for  the  other  under  the  micro- 
scope of  the  comparator  without  requiring  any  change  in  focus. 
When  placed  upon  a  plane  surface  every  part  of  the  upper  surface 
was  found  to  remain  in  focus  during  a  movement  of  the  microscope 
carriage  over  the  entire  length. 

In  all  of  these  bars,  however,  it  was  found  to  be  necessary  to 
provide  for  the  variations  in  the  length  of  the  standard  unit  pro- 
duced by  the  warping  of  the  upper  surfaces,  occasioned  by  the 
flexure  of  the  bars  themselves  whenever  they  do  not  rest  upon  a 
perfectly  plane  surface.  This  is  accomplished  by  supporting  the 
bars  at  two  points  placed  at  a  distance  from  the  center  equal  to 
half  the  length  of  the  bar  divided  by  the  square  root  of  3.  If 
the  supports  are  moved  nearer  to  the  center  of  the  bar  the  upper 
surface  becomes  more  convex  and  the  lower  surface  more  con- 
cave. If  they  are  placed  nearer  the  ends,  the  reverse  effect 
takes  place.  According  to  the  investigations  of  Airy,  Clarke, 
and  others,  the  least  effect  of  a  warped  surface  in  producing  a 
change  in  the  length  of  the  whole  unit  will  take  place  when  the 
supports  are  placed  at  the  neutral  points  whose  distance  apart 

should  be 

Length  of  bar. 

V  n*  —  l 
in  which  n  represents  the  number  of  supports. 

Aside  from  the  neutralization  of  the  effect  of  the  flexure  of 
the  bar  by  the  location  of  the  points  of  support,  this  method  of 
two  supports  has  a  decided  advantage  over  the  support  upon  a 
supposed  plane  surface,  from  the  fact  that  although  the  bar  may 
be  ordinarily  kept  in  a  vertical  position,  whenever  it  is  placed 
upon  its  supports  at  the  neutral  points  it  will  fall  into  an  invari- 
able plane  within  a  very  short  time. 

As  an  illustration  of  the  necessity  of  attention  to  the  question 


of  change  of  length  through  flexure,  it  may  be  stated  that  the 
deviation  in  the  length  of  the  yard  upon  P.  &  W.2,  when  the 
supports  are  placed  at  the  extreme  ends  of  the  bar,  is  over  one 
thousandth  of  an  inch. 

If  the  defining  lines  are  traced  in  the  neutral  plane  of  the  bar, 
the  effect  of  flexure  will  be  practically  eliminated.  Hence  in 
P.  &  W.j  the  yard  is  traced  upon  the  polished  surfaces  of  gold 
plugs  inserted  in  the  bottom  of  wells  sunk  to  the  middle  of 
the  bar.  This  form  has  certain  advantages  for  standards  in 
which  the  total  length  is  the  main  consideration,  but  it  has  the 
decided  disadvantage  of  requiring  the  use  of  an  objective  of  low 
power;  besides,  only  the  larger  subdivisions  of  the  entire  unit 
can  be  obtained. 

But  there  is  a  very  simple  way  of  avoiding  the  effect  of  flexure 
upon  surface  graduations.  As  the  writer  has  nowhere  seen  an 
account  of  the  method  which  he  has  found  very  successful  in 
practice,  it  will  be  briefly  described.  The  bed  of  the  comparator 
is  first  carefully  leveled  up.  A  shallow  pan  containing  a  thin 
layer  of  mercury  is  placed  upon  the  surface  of  the  bed-plate  and 
extends  its  entire  length.  The  microscope,  after  being  focussed 
directly  upon  the  surface  of  mercury  at  one  end,  is  then  carried 
along  the  ways  to  the  other  end.  If  the  surface  of  the  mercury 
remains  in  focus  at  every  point,  the  microscope  plate  moves  in  an 
invariable  plane.  By  a  movement  of  the  flexure  screws  the  bed 
plate  can  be  easily  and  quickly  adjusted  so  that  this  condition 
will  be  satisfied. 

As  a  further  test  Messrs.  Alvan  Clark  &  Sons  have  prepared 
for  me  a  bar  having  nearly  an  optically  plane  surface  when  sup- 
ported at  the  neutral  points.  It  is  always  found  that  when  the 
bed-plate  has  been  Adjusted  to  the  mercury  surface,  every  point 
of  the  surface  of  this  test-bar  also  remains  in  focus. 

Having  made  sure  that  the  microscope  plate  moves  in  an  in- 
variable plane,  we  have  only  to  stone  the  plugs  which  receive  the 
graduations  until  they  are  in  the  same  focal  plane ;  the  bar  mean- 
while resting  upon  its  supports  at  the  neutral  points.  It  is 
obvious  that  whenever  the  bar  is  supported  at  these  points  the 
polished  surface  of  the  plugs  will  always  fall  into  the  same 
plane,  unless  a  permanent  "set"  should  take  place,  of  which 
there  is  no  present  evidence. 


8 

CONSTRUCTION    OF    STANDARDS. 

Since  it  is  desirable  that  the  final  standard  shall  have  as  small 
errors  as  possible,  the  plan  was  adopted  of  tracing  upon  P.  &  W.0 
a  provisional  yard  in  order  that  its  relation  to  "Bronze  11" 
might  be  obtained.  With  the  corrections  thus  obtained,  P.  &  W.j 
could  be  constructed  independently  of  the  variations  of  tempera- 
ture. Then,  having  prepared  the  surface  of  P.  &  W.2  anew, 
P.  &  "W.j  could  be  made  available  in  laying  off  the  final  yard 
upon  this  bar. 

Professor  Hilgard,  Superintendent  of  the  Bureau  of  Weights 
and  Measures,  kindly  offered  to  undertake  the  final  comparisons 
with  "  Bronze  11."  He  also  placed  at  my  disposal  the  various 
standards  of  the  Bureau.  It  seemed  necessary  to  transfer  my 
comparator  to  Washington,  in  order  that  the  standards  in  my  pos- 
session might  be  compared  with  the  standards  of  the  Bureau  under  the 
same  conditions  as  would  exist  in  the  subsequent  comparisons  at 
Cambridge. 

Inasmuch  as  the  comparator  of  the  Bureau  is  what  is  known 
as  a  vertical  comparator,  in  which  the  graduated  surface  is  in  a 
vertical  plane  when  the  bar  is  placed  in  a  horizontal  position  for 
comparison,  while  in  all  of  my  comparisons  the  graduated  sur- 
face is  in  a  horizontal  plane,  it  seemed  desirable  to  accept  the 
facilities  which  the  Bureau  so  kindly  offered.  In  a  subsequent 
paper  I  shall  enter  into  a  critical  examination  of  the  relative 
advantages  of  these  two  forms  of  comparators,  employing  data 
which  the  new  comparator  has  furnished,  since  in  this  instrument 
the  two  forms  are  interchangeable.  My  present  impression  is 
decidedly  in  favor  of  the  vertical  form.  It  is  to  be  remarked  in 
this  connection  that  the  vertical  comparator  recently  described 
by  Professor  Wild,  of  the  Central  Physical  Observatory  of  St. 
Petersburg,  was  anticipated  by  the  Lane  comparator  at  Wash- 
ington, which  has  been  in  actual  use  for  several  years. 

Having  traced  upon  P.  &  W.2  a  provisional  yard  in  the  man- 
ner already  described,  the  bar  was  sent  to  Washington  for  com- 
parison with  "  Bronze  11."  According  to  the  report  of  Professor 
Hilgard,  this  yard  was  found  to  be  25  millionths  of  an  inch  longer 
than  "  Bronze  11."  Since  "  Bronze  11 "  is  88  millionths  of  an 
inch  shorter  than  the  Imperial  Yard,  this  provisional  yard  was 
therefore  63  millionths  of  an  inch  shorter  than  the  Imperial 


9 

Yard.     Of  course  this  very  close  agreement  was,  to  a  certain  ex- 
tent, accidental. 

Having  this  standard  as  a  basis,  it  was  now  possible  to  disre- 
gard in  a  large  measure  the  question  of  temperature  in  the  trans- 
fers to  P.  &  W.j  and  from  P.  &  W.t  back  to  P.  &  Wa.  In 
making  these  transfers  an  attempt  was  made  to  make  P.  &  W.3 
equal  to  the  Imperial  Yard  No.  1,  and  to  make  P.  &  W.x  equal 
to  "  Bronze  11." 

In  P.  &  W.j  there  are  several  groups  of  three,  four,  and  five 
lines  each.  As  it  was  necessary  to  employ  a  special  device  in 
tracing  the  lines  at  the  bottom  of  the  wells,  which  could  only  be 
tested  by  actually  ruling  the  lines,  it  was  found  necessary  to  ex- 
periment upon  the  surfaces  of  the  gold  plugs.  The  defining  lines 
of  this  yard  are  the  middle  lines  of  the  group  of  five  lines  nearest 
the  inner  edge  of  the  plugs.  (Fig.  3,  p.  24.)  In  P.  &  W.2  there 
are  three  lines  on  each  plug,  ruled  at  intervals  of  one  thousandth 
of  an  inch.  The  middle  lines  are  taken  as  the  defining  lines. 

The  temperature  of  the  comparing-room  having  been  brought 
as  near  to  62°  as  possible,  the  yard,  with  the  same  subdivisions 
as  on  P.  &  W.j  and  P.  &  W.2  was  then  transferred  to  the  sur- 
face of  P.  &  W8. 

Simultaneously  with  these  transfers,  the  defining  lines  of  the 
meter  at  62°  Fahr.  were  drawn  by  making  the  length  168.3 
mikrons  longer  than  the  Tresca  meter. 

In  grinding  the  end-measures  to  length,  I  have  employed,  with 
good  success,  the  very  simple  device  furnished  me  by  you  for 
the  purpose.  Bar  P.  &  W.3  was  originally  left  by  your  work- 
men only  a  trifle  longer  than  the  normal  length,  so  that  it  was 
found  necessary  to  carry  the  grinding  beyond  the  normal  length 
in  order  to  make  the  end  faces  parallel.  In  this  way  both  the 
yard  and  the  meter  were  made  too  short  by  an  appreciable 
amount.  Inasmuch  as  the  end-measures  are  useful  only  as  orig- 
inal standards  of  comparison,  a  slight  error  is  of  no  account, 
provided  it  is  known  with  certainty  and  is  constant. 

The  precautions  required  in  grinding  to  the  correct  length  at 
a  given  temperature  are  so  many  that  considerable  labor  is  in- 
volved in  the  operation.  The  required  length  is  first  brought  to 
within  about  one  thousandth  of  an  inch.  During  this  operation 
a  nearly  constant  temperature  is  maintained  by  the  immersion  of 


10 

both  the  comparing  and  the  compared  bars  in  the  same  liquid. 
When  the  bars  are  taken  from  the  liquid  and  compared  in  air, 
one  is  liable  to  be  deceived  by  an  apparent  change  in  their 
lengths,  due  to  the  unequal  effect  of  evaporation  upon  the  two 
bars.  Unless  the  bars  have  the  same  shape  this  action  is  very 
noticeable.  On  this  account  alone,  a  leeway  of  y-J^  of  an  inch  is 
none  too  great. 

A  series  of  comparisons  in  air  is  now  made  with  the  standard 
extending  over  a  period  of  from  ten  to  fifteen  days,  and  under 
temperatures  ranging  as  far  below  and  as  far  above  62°  as  pos- 
sible. The  correction  thus  obtained  is  taken  as  the  basis  of  the 
estimate  of  the  amount  which  may  safely  be  taken  off  in  the 
next  operation.  Usually  two  or  three  operations  will  be  found 
necessary  before  the  true  limit  is  reached,  each  requiring  an  in- 
vestigation of  the  relation  between  the  comparing  and  the  com- 
pared bars.  When,  however,  the  relative  coefficient  of  expan- 
sion between  the  two  bars  is  known,  three  or  four  days  will  be 
sufficient  for  each  series  of  comparisons. 

On  the  21st  of  January,  1881,  comparator  No.  1,  belonging  to 
the  writer,  was  shipped  to  Washington,  the  temporary  bed-plate 
for  mounting  it  having  been  previously  forwarded  from  your 
establishment. 

On  the  evening  of  the  same  day,  I  started  for  the  same  des- 
tination, taking  with  me  the  Tresca  meter  and  bars  P.  &  WM 
P.  &  W.2  and  P.  &  W3.  Arriving  at  Washington  on  the  23d 
instant,  everything  was  found  to  be  in  readiness  for  the  work  of 
comparison.  My  comparator  was  assigned  to  room  96,  in  which 
a  pretty  steady  high  temperature  could  be  maintained. 

The  comparisons  which  the  Bureau  were  to  undertake  with 
the  Lane  comparator  were  committed  to  the  care  of  Assistant 
Edwin  Smith.  It  was  arranged  by  Professor  Hilgard  that  I 
should  make  alternate  readings  of  the  microscopes  with  Mr. 
Smith.  With  this  exception,  all  the  operations  of  comparison 
were  conducted  by  Mr.  Smith.  Indeed,  a  knowledge  of  the 
results  obtained  was  purposely  avoided  during  the  work,  from 
the  fear  that  the  readings  might  be  affected  by  this  knowledge. 

The  comparisons  of  P.  &  W.2  with  "  Bronze  11 "  occupied  three 
days,  from  three  to  four  series  being  taken  each  day  at  intervals 
of  about  two  hours.  The  comparison  of  P.  &  W.j  with  "  Bronze 


11 

11"  also  occupied  three  days,  the  order  of  observations  and  con- 
ditions of  temperature  being  nearly  the  same  as  with  P.  &  W2. 

During  the  afternoon  of  January  29th  my  comparator  was 
removed  to  the  Observatory,  a  nearly  isolated  small  brick  build- 
ing, which  served  an  admirable  purpose  for  comparisons  at  a  low 
temperature.  Two  vacant  transit  piers  gave  a  very  steady  sup- 
port to  the  comparator. 

Bars  P.  &  W.3  and  the  Tresca  meter  were  at  the  same  time 
removed  to  the  building  and  placed  in  position  for  comparison. 
From  this  time  till  the  afternoon  of  February  2d  a  very  steady, 
low  temperature  was  maintained  in  the  building.  During  Jan- 
uary 30th,  31st,  and  a  part  of  February  1st,  comparisons  were 
made  between  these  bars.  During  the  afternoon  of  January  31st 
"Bronze  11 ",  P.  &  W.j  and  P.  &  W.2  were  removed  to  the  Ob- 
servatory and  placed  in  position  for  comparison  ;  the  comparisons 
of  these  bars  upon  the  Lane  comparator  having  now  been  com- 
pleted. During  February  1st  and  February  2d  these  bars  were 
compared  by  Mr.  Smith  and  myself,  according  to  a  scheme  simi- 
lar to  that  observed  with  the  vertical  comparator. 

At  4  o'clock  in  the  afternoon  of  February  2d  the  comparator 
and  all  the  bars  were  again  removed  to  room  96,  in  which  the 
temperature  was  now  not  far  from  62°  Fahr.  During  February 
4th,  6th,  and  7th  especial  attention  was  given  to  the  comparisons 
between  "  Bronze  11 ",  P.  &  W.j  and  P.  &  \V.2  with  reference  to 
the  determination  of  their  relative  coefficients  of  expansion. 

After  my  return  from  Washington  an  extended  series  of  com- 
parisons was  made  between  meter  P.  &  W.t  and  the  Tresca  meter 
T%;  between  the  end-meter  P.  &  W.3  and  the  Froment  meter 
designated  (Rj)*;  between  yard  and  meter  P.  &  W.j  and  the  line- 
yard  and  meter  of  P.  &  W.3 ;  between  yard  P.  &  "W.j  and  the 
Whitworth  yard  (W.),  and  between  (W.),  P.  &  W.3  and  P.  &  W.4 ; 
both  for  the  yard  and  the  meter. 

COEFFICIENTS    OF    EXPANSION. 

In  order  to  transfer  the  standard  yard  from  the  bronze  bar  to 
a  bar  of  any  other  metal,  it  is  necessary  to  know  either  the  abso- 
lute coefficient  of  expansion  of  the  normal  bar,  or  the  relative 
expansion  of  the  two  bars  compared.  The  relative  coefficients 
of  expansion  between  the  several  bars  may  be  obtained  from  the 

*  See  pages  289-293,  Proc.  American  Academy. 


12 

comparisons  themselves.  It  is  therefore  necessary  to  obtain  the 
absolute  coefficient  of  at  least  one  of  the  bars. 

At  the  International  Bureau  of  Weights  and  Measures,  and  at 
the  Standards  office  in  London,  comparisons  are  for  the  most 
part  made  at  air  temperatures.  At  Washington,  however,  the 
preference  is  given  to  liquid  contacts,  the  bars  to  be  compared 
being  immersed  in  flowing  glycerine.  After  considerable  experi- 
ence with  both  methods,  I  am  still  in  doubt  which  is  capable  of 
the  most  accurate  results.  In  the  operations  connected  with  the 
construction  and  verification  of  standard  gauges,  however,  you 
unquestionably  require  air  contacts.  I  have  therefore  deter- 
mined the  coefficients  under  these  conditions. 

At  the  outset  of  this  investigation  a  difficulty  was  encountered 
which  at  first  appeared  insurmountable  with  the  means  of  con- 
trolling temperature  at  my  command.  In  comparing  the  Tresca 
bar  Ta2  which  has  a  small  mass,  with  P.  &  W.2  which  has  a 
mass  several  times  greater,  it  was  found  that  the  slightest  change 
in  temperature  would  change  their  relative  lengths  by  an  amount 
far  greater  than  that  due  to  the  coefficient  of  expansion  between 
them.  I  add  one  or  two  examples  :  On  one  occasion  after  the 
bars  had  remained  at  the  nearly  constant  temperature  of  78°  for 
several  hours,  one  of  the  windows  of  the  comparing  room  was 
opened  for  thirty  seconds  and  then  closed  again.  The  tempera- 
ture of  the  outside  air  was  20°.  The  two  bars  were  then  com- 
pared again,  the  operation  requiring  about  forty  seconds.  Dur- 
ing this  time  Ta2  had  lost  on  P.  &  W.2  no  less  than  468  mil- 
lionths  of  an  inch.  Under  the  normal  condition  of  the  two  bars 
P.  &  W.2  should  have  shortened  faster  than  Ta2  under  the  sup- 
position that  both  had  the  same  form  and  the  same  mass.  As 
another  illustration,  I  take  the  comparison  of  P.  &  W.3  with  Ta2 
made  February  24,  1881.  These  bars  have  as  their  relative 
coefficient  130  millionths  of  an  inch  for  each  degree  Fahrenheit. 
The  temperature  of  the  comparing  room  had  been  maintained  at 
82°  for  several  hours.  The  temperature  of  the  outside  air  was 
about  25°. 

In  the  column  of  P.  &  W.3  minus  Ta2,  are  given  the  number 
of  millionths  of  an  inch  which  Ta2  had  gained  over  P.  &  W.3  at 
the  times  given.  Both  windows  of  the  cornparing-room  were 
opened  wide  at  3  hours,  55  minutes,  0  seconds. 


Thermometer. 

(P.  &W.8)-(T«2) 

o 

div. 

78.0 

+1672 

68.0 

+  5105 

59.4 

+4413 

-       60.4 

+  4057 

60.7 

+3723 

64.9 

—    58 

64.8 

—    76 

63.9 

—    63 

62.2 

—    73 

60.6 

—  136 

57.2 

—  132 

13 

Time. 
h.    m.     s. 
3    55    35 
3    57    15 

3  58    45 
410 

4  2  35 
4  12  45 
4  14  45 
4  17  5 
4  20  15 
4  26  25 
4  28  5 

It  will  be  seen  from  the  above  that  in  35  seconds  Ta2  fell 
behind  P.  &  W.3  no  less  than  1672  millionths  of  an  inch,  that 
within  two  minutes  the  maximum  deviation  took  place  and  that 
after  this  time  P.  &  W.3  continued  to  shorten  faster  than  Ta2  but 
with  a  rapidly  diminishing  ratio  of  decrease. 

Suppose  I  place  a  bar  of  glass  of  large  mass  which  has  a 
very  low  coefficient  of  expansion  upon  the  comparator,  and 
place  beside  it  a  narrow  and  deep  bar  of  zinc  which  has  a  very 
high  coefficient  of  expansion.  Suppose  a  steady  low  tempera- 
ture has  been  maintained  in  the  comparing-room  for  a  sufficient 
length  of  time  for  each  bar  to  settle  to  its  normal  length  at  a 
given  constant  temperature.  Under  these  conditions  I  suddenly 
introduce  into  the  comparing-room  a  volume  of  heated  air  and 
maintain  as  nearly  as  possible  a  constant  supply.  The  effect  of 
this  change  of  temperature  upon  the  bars  will  be  nearly  as 
follows:  . 

(1)  Within  ten  minutes  the  zinc  bar  will  increase  in  length 
by  the  total  amount  due  to  the  change  in  temperature,  and  any 
further  slight  changes  in  temperature  in  the  surrounding  air  will 
produce  their  normal  effect  in  from  five  to  eight  minutes. 

(2)  The  heat  will  penetrate  the  glass  bar  very  slowly,  probably 
in  nearly  parallel  waves.     Ten  or  fifteen  minutes  will  elapse  be- 
fore any  change  of  length  will  be  noticeable.     From  this  point  the 
changes  which  occur  will  be  very  irregular,  ^specially  if  there 
are  changes  in  the  temperature  of  the  surrounding  air.     While 
that  portion  of  the  heat  which  has  been  already  absorbed  is  doing 
its  work  the  changes  in  the  temperature  of  the  surrounding  air 
will  produce  their  effect  upon  the  outside  portions  of  the  bar. 


14 

These  pulsations  will  go  on  in  waves  of  constantly  diminishing 
amplitude  until  there  is  an  equilibrium  of  temperature  between 
all  the  parts  of  the  bar. 

It  is  impossible  to  predict  in  any  assumed  case  the  length  of 
time  required  for  a  condition  of  equilibrium  between  the  zinc 
and  the  glass  bars.  In  general,  the  greater  the  range  of  tem- 
perature and  the  greater  the  fluctuations  during  the  passage  from 
one  extreme  to  the  other,  the  longer  will  be  the  time  required  for 
the  restoration  of  the  equilibrium.  It  cannot  be  safely  placed  at 
less  than  four  hours. 

All  of  my  observations  show  that  the  changes  in  the  length  of 
a  bar  under  a  varying  temperature  are  due  to  two  causes. 

(a)  The  direct  action  of  heat  upon  the  surfaces  of  the  bar. 

(b)  The  action  of  heat  already  absorbed  in  the  body  of  the 
bar  and  wrhich  is  not  indicated  by  the  ordinary  thermometer. 

The  amount  of  this  absorbed  heat  will  be  a  direct  function  of 
the  conductive  power  of  the  metal  and  the  mass  of  the  bar. 

Changes  of  considerable  magnitude  have  been  repeatedly  ob- 
served in  the  relative  lengths  of  two  bars  having  a  large  mass, 
notwithstanding  the  fact  that  the  reading  of  the  thermometer 
placed  upon  the  surface  of  the  bar  remained  constant  during  the 
continuation  of  the  observations. 

The  influence  of  mass  in  retarding  the  action  of  temperature 
has  one  compensation.  If  the  standard  bars  having  the  shape 
and  size  of  "  Bronze  11 "  are  kept  in  a  room  from  which  direct 
sunlight  is  excluded,  and  in  which  a  nearly  constant  temperature 
is  maintained,  the  presence  of  the  observer  will  have  no  effect 
upon  comparisons  if  they  do  not  occupy  over  fifteen  or  twenty 
minutes.  During  this  time  the  bars  may  be  handled,  almost  with 
impunity,  if  the  hands  are  protected. 

The  general  law  under  which  these  variations  take  place  may 
be  stated  as  follows :  The  time  required  by  bars  of  different 
metals  to  assume  their  normal  length  under  great  changes  of 
temperature,  is  a  function  of  their  shape  and  mass. 

Further  observations  in  this  direction  are  needed,  but  the  time 
required  seems  to  vary  from  twenty-five  minutes  for  the  copper 
(Tresca)  meter  to  four  and  a  half  hours  for  the  bronze  bars. 

In  these  observations  the  ordinary  practice  of  placing  the  ther- 
mometer upon  the  upper  surface  of  the  bar  compared  has  been 


15 

followed.  At  London,  the  thermometers  rest  upon  the  surface 
of  the  bar  measured,  but  shields  of  the  same  metal  are  placed 
over  the  bulbs.  At  Paris,  the  same  plan  is  followed,  except  that 
no  shields  are  used.  At  Washington  shields  are  used,  but  they 
are  not  made  of  the  same  material  as  the  bars.  Whenever  a 
nearly  constant  'temperature  can  be  maintained,  as  is  the  case  at 
Paris,  the  thermometers  indicate  nearly  the  temperature  of  the 
bar  upon  which  they  are  placed. 

But  it  must  be  borne  in  mind  that  the  thermometer  indicates 
only  its  own  temperature.  Whenever  a  sudden  change  of  tem- 
perature is  indicated,  it  cannot  be  inferred  that  there  is  a  corre- 
sponding change  in  the  length  of  the  bar  to  which  it  is  attached. 

Many  experiments  have  been  made  during  the  last  three  years 
for  the  purpose  of  determining  within  what  limits  small  changes 
of  temperature  in  the  com  paring-room  can  be  neglected  in  the 
comparison  of  standards.  When  the  observer  first  enters  the 
comparing-room  at  Cambridge,  where  the  temperature  is  consid- 
erably below  the  normal  temperature  of  his  person,  the  thermom- 
eter will  usually  indicate  an  increase  of  temperature  amounting 
to  0.5°  within  five  minutes.  What  ivill  be  the  effect  of  this  increase 
in  changing  the  length  of  the  bar  within  the  same  limits  of  time  ?  Here, 
again,  the  effect  will  be  a  function  of  the  shape  and  the  mass  of 
the  bar.  The  writer  has  at  the  present  time  strips  of  steel  and 
of  aluminum  forty  inches  long,  one  inch  wide,  and  four  one 
thousandths  of  an  inch  thick,  mounted  horizontally  upon  the 
comparator.  These  strips  are  placed  side  by  side,  a  very  narrow 
space  intervening.  They  are  fastened  at  one  end,  and  are  kept 
taut  by  springs  attached  to  the  other  end.  It  is  obvious  that  the 
relative  positions  of  the  two  parts  of  a  line  drawn  across  the  face 
of  the  strips  at  a  given  temperature  will  indicate  the  relative  varia- 
tions in  the  length  of  the  strips  under  varying  temperatures. 
These  variations  are  measured  under  the  microscope  of  the  com- 
parator. Under  this  arrangement  the  strips  become  a  metal 
thermometer. 

It  has  been  found  that  very  slight  changes  in  temperature  are 
practically  registered  instantaneously  by  the  change  in  the  posi- 
tion of  the  two  lines.  When  the  air  in  the  room  is  set  in  motion 
by  swinging  the  door  of  the  comparing-room,  the  corresponding 
swaying  of  the  lines  back  and  forth  furnishes  a  beautiful  illustra- 


16 

tion  of  the  instantaneous  effect  of  a  change  of  temperature  upon 
a  body  having  a  large  surface  area  and  a  very  small  mass.  In 
this  case  it  is  impossible  to  make  the  reading  of  the  micrometer 
of  the  microscope  before  the  effect  of  the  presence  of  the  observer 
will  be  visible. 

When  we  pass  to  the  Tresca  standard,  which  has  a  large  sur- 
face area  and  a  small  mass,  experiment  has  shown  conclusively 
that  the  effect  of  the  presence  of  the  observer  can  be  neglected 
for  about  three  minutes.  In  the  case  of  standards  having  the  shape 
and  mass  of  P.  &  W.2,  i.  e.,  a  cross  section  of  1  inch,  or  even  a 
cross  section  of  1-J-  X  i  inches,  it  has  been  found  that  the  presence 
of  the  observer  in  the  comparing-room  can  be  neglected  for  fifteen 
minutes,  provided  there  is  no  direct  contact  between  the  person  of  the 
observer  and  the  bar.  When  there  is  a  direct  contact  through  the 
hands,  continuing,  e.  g.,  for  one  minute,  there  will  be  an  instan- 
taneous change  in  length,  especially  if  there  is  moisture  on  the 
hands,  but  if  no  other  contacts  are  made,  there  will  be  no  visible 
shortening  of  the  bar  for  five  minutes,  and  the  total  dissipation 
of  the  heat  stored  in  the  bar  by  the  contact  wrill  require  from 
twenty  to  twenty -five  minutes.  If  a  shield  of  thick  writing  paper 
is  used  the  bar  can  be  handled  without  producing  any  visible 
effect,  at  least  for  several  minutes.  The  practical  conclusion  to 
be  drawn  from  these  observations  is :  first,  that  all  comparisons 
of  standards  should  be  completed  before  the  presence  of  the  ob- 
server can  produce  any  effect  in  changing  the  length  ;  and  second, 
that  no  further  comparisons  should  be  made  until  the  small 
amount  of  heat  which,  though  imperceptible  at  the  time,  has  in 
reality  been  imparted  to  the  bars,  has  been  merged  in  the  general 
temperature  of  the  entire  mass.  In  general,  all  comparisons  have 
been  completed  within  ten  minutes,  and  at  least  four  hours  have 
been  allowed  to  intervene  between  the  comparisons. 

Several  other  necessary  precautions  have  been  taken  in  relation 
to  the  temperature. 

First.  The  number  of  comparisons  at  equal  distances  below  and 
above  62°  have  been  made  as  nearly  equal  as  possible,  thus  elim- 
inating to  a  certain  extent  at  62°,  the  effect  of  errors  introduced 
through  the  temperature. 

Second.  Although  the  reading  of  a  thermometer  may  seem  to 
be  stationary,  it  in  reality  has  a  drift,  either  up  or  down,  which 


17 

may  be  ascertained  by  subsequent  readings.  It  lias  been  my  aim 
to  obtain,  in  every  series  of  comparisons,  nearly  an  equal  number 
of  cases  of  upward  and  downward  drifts.  It  should  be  said  here, 
the  reading  of  the  thermometer  adopted  is  always  that  which  is 
taken  wThen  the  observer  first  enters  the  com  paring-room. 

Third.  It  has  been  found  that  this  elimination  of  errors  for 
drifts  of  short  period  is  not  perfectly  effected,  but  that  there  are 
drifts  of  long  period  which  are  functions  of  the  season  of  the 
year.  The  effect  of  errors  produced  by  this  cause,  is  impercepti- 
ble except  by  the  comparison  of  long  series  of  observations  made 
at  opposite  seasons  of  the  year.  The  delay  in  completing  this 
report  has  been  occasioned  by  the  necessity  of  continuing  com- 
parisons of  this  character.  It  is  believed  that  the  results  to  be 
given  hereafter  in  this  report  are  practically  free  from  errors  of 
the  nature  indicated. 

I  notice  at  this  point  one  other  precaution  which  must  always 
be  taken  against  a  very  fruitful  source  of  error.  I  refer  to  the 
error  introduced  through  an  imperfect  determination  of  the  focal 
distance  of  the  objective  of  the  microscope  in  making  the  com- 
parisons. With  heavy  lines,  having  rounded  edges,  it  is  well 
nigh  impossible  to  focus  upon  the  defining  lines  twice  alike.  The 
error  which  may  be  introduced  in  this  way  may  be  as  great  as 
-g-J-Q-u  of  an  inch  in  a  yard.  The  most  effective  remedy  against 
this  difficulty  is  the  selection  of  a  very  fine  scratch  upon  the  sur- 
face for  the  determination  of  the  proper  focus.  The  correct  focal 
distance  can  be  found  from  fine  lines  much  more  accurately  than 
from  coarse  ones. 

It  is  obvious,  in  view  of  what  has  been  said,  that  observations 
for  the  determination  of  the  coefficients  of  expansion  have  a  de- 
finite value  only  when  the  bars  reach  a  state  of  absolute  rest 
under  a  constant  temperature,  and  when  all  the  precautions  above 
described  have  been  taken. 

Three  series  of  determinations  of  the  absolute  coefficient  of 
expansion  of  P.  &  W.2  and  of  T  have  been  made. 

In  the  first  series  a  normal  bar  was  kept  in  the  clock-room  of 
the  Observatory,  in  which  the  temperature  rarely  varied  more 
than  1°  or  2°  during  twenty-four  hours.  At  an  early  morning 
hour,  this  bar  was  carried  into  the  cornparing-room  and  compared 
with  the  bar  whose  coefficient  was  required.  The  time  required 


18 

to  make  the  comparison  was  usually  about  forty  seconds.  After 
the  comparison,  the  normal  bar  was  immediately  returned  to  the 
clock-room. 

In  the  second  series,  P.  &  W.a  was  immersed  in  water,  at  a 
temperature  varying  between  32°  and  90°  Fahrenheit. 

The  common  unit  of  comparison  was  the  constant  distance 
between  the  stops  of  the  comparator.  While  the  results  obtained 
by  this  method,  from  observations  on  the  same  day,  were  found 
to  have  a  close  agreement,  the  results  obtained  on  different  days 
were  very  discordant.  It  was  found  to  be  impossible  to  maintain 
at  the  same  temperature,  the  entire  mass  of  the  water  surrounding 
the  bar. 

A  new  method  of  maintaining  the  entire  mass  of  a  liquid  at  a 
constant  temperature  has  been  recently  introduced  at  Paris  and 
London  with  success.  Doubtless  very  accordant  results  will  be 
obtained  from  this  method,  but  after  all,  immersion  in  a  liquid  is 
not  the  normal  condition  in  which  standards  are  used  in  ordinary 
practice,  and  therefore  the  coefficient  obtained  in  this  way  does 
not  represent  the  conditions  which  are  the  most  likely  to  occur  in 
daily  experience.  The  coefficient  of  expansion  ought  to  be  obtained 
under  the  ordinary  conditions  under  which  the  standard  is  used  in 
measurements  of  length. 

It  is  believed  that  the  difficulties  inherent  in  the  methods 
described,  are  overcome  in  the  third  method  adopted.  An  end- 
measure  bar  of  steel  was  mounted  in  a  metal  box  in  such  a 
manner  that  there  was  freedom  of  motion,  longitudinally, 
under  variations  of  temperature.  The  ends  of  the  bar  were  of 
hardened  steel.  They  project  beyond  the  ends  of  the  box  about 
one-fourth  of  an  inch.  This  box,  filled  with  ice  and  water  which 
covered  the  bar  to  the  depth  of  about  five  inches,  was  supported 
upon  the  bed  of  the  comparator  in  such  a  manner  that  one  end 
of  the  bar  was  in  contact  with  a  fixed  stop  attached  firmly  to  the 
bed  plate.  A  corresponding  stop  was  attached  to  the  carriage 
which  carries  the  microscope.  Meter  P.  &  W.2  was  mounted 
permanently  upon  the  bed  of  the  comparator  in  a  line  parallel 
with  the  stops,  and  was  adjusted  for  parallelism  with  respect  to 
the  microscope  carriage  in  both  vertical  and  horizontal  planes. 
The  observations  proceed  in  the  following  order : 

(a)     After  the  movable  and  the  fixed  stops  have  been  brought 


19 

into  contact,  the  microscope  is  adjusted  upon  the  initial  defining 
line  at  one  end  of  the  meter.  The  microscope  carriage  is  then 
moved  forward  far  enough  to  allow  the  box  containing  the  end- 
meter  in  melting  ice,  to  be  placed  in  position  against  the  fixed 
stop.  The  movable  stop  is  then  brought  into  contact  with  the 
other  end  of  the  bar  by  a  movement  of  the  carriage.  If  the  two 
bars  have  the  same  length,  the  micrometer  line  of  the  microscope 
should  fall  upon  the  defining  line  of  the  meter  at  this  end. 
Whatever  the  relation  existing  between  the  length  of  the  two 
standards,  the  difference  is  measured  with  the  micrometer  screw. 
The  ice-box  is  then  removed  and  the  observation  is  not  repeated 
until  the  required  conditions  which  relate  to  temperature  are 
fulfilled.  It  will  be  seen  that  whatever  the  temperature  of  the 
com  par  ing-room,  the  line-measure  standard  is  referred  to  a  con- 
stant unit  of  length.  Hence,  the  difference  in  the  length  of  the 
standards  at  known  temperatures,  divided  by  the  difference  of  the 
corrected  readings  of  the  thermometer  will  give  the  absolute  co- 
efficient of  expansion  for  the  bronze  bar. 

The  absolute  coefficient's  of  three  bars  have  been  determined 
in  the  manner  above  described,  viz.:  P.  &  W.2,  the  Coast  Sur- 
vey meter  designated  C.  S.,  and  the  Tresca  meter  T.  For  the  low 
temperatures  nearly  all  the  observations  were  made  a  little  before 
sunrise ;  the  windows  of  the  comparing-room  having  been  left 
open  during  the  night.  For  the  high  temperatures,  a  gas  stove 
was  used  to  maintain  a  constant  supply  of  heat.  It  was  found 
to  be  possible  to  keep  the  temperature  of  the  comparing-room  at 
about  80°  for  several  days  with  an  extreme  variation  not  exceed- 
ing one  or  two  degrees. 

The  observations  upon  the  bar  T  extend  from  February  7, 
1883,  to  May  8,  1883;  those  upon  bar  C.  S.  from  February  12, 
to  May  18, 1883,  and  those  upon  P.  &  W.2  from  February  12, 
to  May  8,  1883. 

The  details  of  these  observations  are  given  in  the  Proceedings 
of  the  American  Academy,  pp.  371-380.  It  will  be  sufficient  to 
give  here  the  results  of  the  groups  of  observations  made  near  the 
temperature  32°  and  62°  Fahr.,  as  shown  on  page  377  etseq.  The 
comparisons  for  each  group  have  all  been  reduced  to  32°  and  62° 
by  means  of  the  provisional  relative  coefficients  previously  found 
between  the  standards  and  the  steel  bar  S  in  melting  ice.  The 


20 


results  are  expressed  in  divisions  of  the  micrometer,  1  division 
being  =  0.504/4=  0,000020  inch. 


Standards  whose  coefficients 
are  to  be  determined. 

Tb±  =  Tresca  Meter. 

C.  S.          =  Stevens  Institute  Meter. 

P.  &  W.2  =  Pratt  &  Whitney  Meter. 


Provisional  relative 
coefficients. 

Coefficient  =  33.18  div. 
"       =34.63 
"       =34.00 


DETERMINATION  OF  THE  ABSOLUTE  COEFFICIENTS  OF  ME- 
TERS T,  C.  S.,  AND  R2,  FROM  THE  NORMAL  VALUES  FOR  0° 
AND  16°.  67. 

METER  Tbi. 


Date. 

(r-  0°) 

S  —  Tbi   Means  by 
at  32°.  0    Groups. 

Date. 

(16°.  67—  r} 

S  —  T*i 
at  62°.0 

Means  by 
Groups. 

1883. 

o 

div.       div. 

1883. 

o 

div. 

dir. 

Feb.    7 

+  1.76 

+  60.7 

Feb.  11 

+  3.20 

-476.9 

7 

+  3.83 

+  57.8 

19 

—  7.86 

—  480.4 

7 

+  7.60 

+  59.6 

25 

+  9.09 

—  473.2 

8 

—  4.30 

+  65.1 

25 

+  8.36 

—  469.6 

8 

+  1.46 

+  53.8    +59.4 

26 

—  5.70 

—  475.6 

—  475.1 

9 

—  4.54 

+  61.3 

Mar.    3 

—  2.66 

—  476.8 

12 

-1.78 

+  61.4 

Apr.  15 

—  2.74 

—  472.6 

12 

—  2.96 

+  59.5 

17 

+  4.42 

—  474.9 

12 

—  0.79 

+  59.0 

18 

+  7.53 

—  472.9 

13 

+  1.69 

+  62.2    +60.7 

19 

+  8.03 

—  474.6 

—  474.4 

13 

+  0.12 

+  60.8 

20 

—  1.29 

—  475.3 

13 

+  3.26 

+  65.2 

24 

—  3.80 

—  471.6 

14 

.  —6.50 

+  56.5 

25 

—  3.37 

—  478.4 

15 

+  5.82 

+  57.5 

26 

—  4.59 

—  474.7 

16 

+  0.78 

+  61.0    +60.2 

27 

+  7.65 

—  475.8 

—  475.2 

20 

—  1.92 

+  57.0 

27 

+  0.30 

—  475.3 

25 

+  2.96 

+  63.0 

28 

—  1.87 

—  473.9 

27 

—  6.71 

+  63.1 

29 

+  1.32 

—  473.1 

27 

+  2.91 

+  61.5 

29 

+  0.66 

—  475.1 

28 

—  3.47 

+  63.1    +61.5 

30 

+  0.79 

—  474.4 

—  474.4 

28 

—  0.22 

+  63.0 

30 

—  1.09 

—  475.0 

28 

—  0.71 

+  63.5 

May    1 

—  1.01 

—  472.5 

Mar.    1 

+  3.64 

+  62.1 

1 

+  0.11 

—  476.4 

4 

—  0.35 

+  59.2 

2 

+  7.95 

—  475.1 

5 

—  4.38 

+  66.7    +62.9 

4 

—  1.40 

—  467.4 

-473.3 

5 

—  1.18 

+  65.6 

4 

—  1.49 

—  469.9 

Apr.  22 

+  4.57 

+  59.9 

4 

—  3.45 

—  470.8 

23 

+  5.97 

+  60.9 

6 

+  0.20 

—  472.2 

24 

+  6.02 

+  59.5 

7 

+  8.75 

—  476.8 

25 

+  5.67 

+  60.1    +61.2 

8 

+  3.80 

—  473.6 

—  472.7 

21 

METER  C.  S. 

Date. 

(T  —  0°) 

S  —  Tbi       Means  by                     (16°«7  —  r) 
at  32°.  0         Groups. 

S  —  Tbi      Mean*  by 
at  62°.  0        Groups. 

1883. 

0 

div. 

div. 

1883. 

o 

div. 

div. 

Feb. 

12 

—  6. 

14 

+  483. 

2 

Feb.  26 

—  5. 

29 

—  85.7 

12 

1. 

15 

+  488. 

8 

Mar.    3 

—  2. 

60 

—  95.8 

13 

+  4. 

69 

+  490. 

0 

Apr.  18 

+  7. 

82 

—  89.4 

13 

—  7. 

76 

+  488.3 

19 

—  6. 

21 

—  92.0 

14 

—  4. 

87 

+  490. 

2     +488.1 

20 

-1- 

12 

—  93 

.6       —91.3 

15 

+  6.14 

+  481. 

3 

21 

—  0. 

12 

—  96 

.8 

16 

-1.44 

[+473 

71 

22 

—  7. 

81 

—  97 

.8 

20 
25 

—  2. 

+  1 

96 
75 

[+476.7] 
+  490.4 

25 
25 

—  3. 
—  4 

72 
15 

—  89 
—  91 

.3 
.4 

27 

+  0.67 

[+475. 

4]    +485.8 

28 

—  2 

04 

—  93 

.1       —98.7 

28 

—  2 

58 

+  488.7 

May    1 

—  0.02      —88 

.1 

28 

—  1 

.07 

+  487.4 

2 

—  1.42      —98.8 

28 

—  0 

11 

+  487.1 

2 

—  2.32 

—  96.7 

28 

—  0 

.80 

+  486 

5 

2 

—  2.48 

—  91 

.0 

28 

—  2.33 

+  485.0     +486.9 

S 

—  1.80 

—  99 

.0       —94.7 

28 

—  8 

76 

+  484.0 

3 

—  1 

15 

—  97 

.5 

28 

+  3 

.13 

+  487 

.2 

3 

—  1 

.54 

—  88.8 

Mar. 

1 

+  5 

.65 

+  482.5 

4 

—  1.68 

—  96.7 

4 

—  8 

.06 

+  484.4 

6 

+  0 

17 

—  86 

.1 

4 

—  4 

.40 

+  493.6     +486.3 

6 

—  0 

79 

—  96 

.3 

6 

—  0 

.04 

—  91 

.3       —92.8 

4 

—  0 

.89 

+  484.8 

19 

+  6 

.70 

+  482.7 

Apr. 

22 

+  4.07 

+  482 

.2 

23 

+  5 

.79 

+  485.8 

23 

+  5 

.88 

+  487.3     +484.6 

24 

+  5 

.77 

+  485 

.1 

25 

+  2 

.23 

+  485 

.4 

26 

+  1 

.54 

+  479.0 

i 

27 

+  4 

.97 

+  485 

.9 

May 

2 

+  7 

.55 

+  477 

.0     +482.6 

Date. 

o-- 

S 
METER  I 

5—  P.&W.g  Means  by 
at32°.0          Groups. 

12 

>.  &  w.2 

Date.   (16°67—  r) 

S—  P.&W 
at  62°.0 

.oMeansby 
Groups. 

1883. 

o 

div. 

div. 

1883. 

div. 

Feb.  13 

+  0 

.58 

+  431 

.9 

Feb.  11 

+  3.66 

—  135 

4 

12 

—  i 

.31 

+  429 

.4 

25 

+  8 

.19 

—  131. 

5 

13 

+  1 

.52 

+  421 

.4 

26 

—  3 

.79 

[—152. 

1] 

14 

+  1 

.81 

+  437 

0 

26 

—4 

.36 

—  135. 

0 

15 

+  4 

.89 

+  433 

4     +430.6 

Mar.  31 

—  2 

.57 

—  126. 

0 

—  132.0 

16 

—  2 

.28 

+  419 

2 

May    4 

—  1 

.38 

—  124. 

9 

16 

+  3 

.65 

+  427 

9 

4 

—  3 

.11 

—  136. 

5 

27 

+  3 

.17 

+  429 

6 

4 

—  3 

.27 

—  135. 

4 

27 

+  2 

.05 

+  444 

2 

6 

+  0 

.15 

—  135. 

6 

28 

—  4 

.35 

+  427 

7     +429.7 

8 

+  3 

.75 

—  143. 

3 

—  135.1 

Mar.   2 

+  4 

.27 

+  427. 

9 

3 

+  3 

.25 

+  432. 

4 

7 

+  8.25 

+  426. 

6      +429.0 

Collecting  results,  we  have 


-  For0«C.  Forl6'.67. 

a  =  +  61.0  div.  =  +  30.7  p.  a  =  —  474.2  div.  =  —  2.39.1  p 

Whence  b  —  +  32.10  div.  =  +  16.18  p 

For  S  -  C.  S. 

a  =  +  488.7  div.  =  +  246.3  p  a  =  —  93.1  div.  =    —  46.9  p 

Whence  b  =  -f  34.90  div.  =  -f  17.59  p 

ForS  —  P.  &  W.a 

a  =  -f  429.8  div.  =  -f-  216.6  p  a  =  —  133.6  div.  =  —  67.3  p 

Whence  5  =  -f-  33.80  div.  =  -j-17.04^ 

We  have  therefore,  from  these  absolute  coefficients,  the  follow- 
ing relative  values  : 


From 


Whence  for 


S-T 

S-C.S. 

s_p.  &  w.2 
T-C.S. 

T-P.  &  W.2 
C.S.-P.  &  W., 


£r=-f  16.18 /i 

£=+17.59^ 
$=+17.04,1 

I—  +1.41  p 
5=  +0.86^ 
1=  —0.55/1 


23 

Combining  these  values  with  the  relative  values  found  from 
the  observations  with  the  universal  comparator,  we  have  finally 
the  following  values  for  the  absolute  coefficients  :  — 

Standards.  Coeff.  for  1  Meter.  Coeff.  for  1  Yard. 

T  +  16.18  fi  -fH.SO/i 

C.S.  1!^9±1^17.60  16.09 


=I*.UP 

"21       17.27       17.04 


These  results  are  nearly  identical  with  those  found  for  T  and 
P.  &  W.2  by  the  methods  described  on  page  18.  They  were  as 

follows  : 

For  T,  coefficient  =  16.  56  p 

For  P.  &  W.8,  coefficient  =  17.55  p 

Since  the  publication  of  this  paper,  the  report  of  Dr.  Pernet 
of  the  International  Bureau,  giving  the  determination  of  the  co- 
efficient of  the  bar  C.  S.,  and  of  a  bar  identical  in  form  and 
assumed  to  be  identical  in  composition  with  the  Tresca  bar  Tb, 
has  been  received.  The  following  are  the  results  of  the  various 
determinations  of  the  coefficient  for  each  degree  Centigrade. 
The  number  of  units  given  represents  the  number  of  units  of 
variation  in  100  millions. 

Standard  Bar.  No.  of  units  in  100  millions.  Observer. 

T.  1642  Benoit. 

T.  1618  Rogers. 

C.  S.  1771  Benoit. 

C.  S.  1760  Rogers. 

P.  &W.2  1717  Rogers. 

Comparing  the  results  for  the  bar  of  metal  C.  S.  we  find  a  dif- 
ference of  only  11  parts  irf  100  millions.  In  forming  an  estimate 
of  the  reality  of  these  values,  it  should  be  borne  in  mind  that 
they  are  the  results  of  observations  made  at  different  times,  by 
different  observers,  neither  observer  having  any  knowledge  of  the 
results  obtained  by  the  other,  with  comparators  of  widely  dif- 
ferent forms  of  construction,  by  different  methods  x)f  compari- 
son, and  with  thermometers  which  have  never  been  directly 
compared. 


Ill  the  discussion  of  the  absolute  lengths  of  the  yards  and 
meters,  P.  &  W.j  P.  &  W.a  P.  &  W.,  and  P.  &  W.4  at  62° 
Fahr.,  reference  is  made  to  the  paper  in  the  Proceedings  of  the 
American  Academy  above  quoted  for  a  full  account  of  the  obser- 
vations which  are  there  given  in  detail.  Only  the  general  results 
will  be  given  in  this  report.  The  bar  here  described  as  P.  ifc  AV.2 
is  there  designated  R2a2.  The  official  report  of  Professor  Hil- 
gard,  however,  relating  to  the  comparison  of  the  yards  P.  &  W.j 
and  P.  &  W.a  will  be  given  in  full.  It  is  as  follows  : 

U.  S.  COAST  AND  GEODETIC  SURVEY  OFFICE, 
WASHINGTON,  February  4,  1881. 

PROF.  J.  E.  HILGARD,  Assistant  in  Charge 
U.  S.  Coast  and  Geodetic  Survey  Office. 

Dear  Sir,  —  The  following  report  on  the  comparisons  of  Bronze 
Yards  P.  &  W.  Nos.  1  and  2  with  the  British  Bronze  Yard 
No.  11,  is  respectfully  submitted. 

These  two  bars  were  brought  to  the  office  on  Jan.  21st  by  Prof. 
Wm.  A.  Rogers,  who  gives  the  following  description  of  them  : 

"P.  &  W.  No.  1  is  a  bronze  bar  of  the  same  composition, 
shape,  and  dimensions  as  the  British  Bronze  Yard  No.  11.  The 
defining  lines  are  ruled  on  gold  plugs  in  wells  one-half  inch  in 
diameter  and  half  the  depth  of  the  bar.  There  are  four  wells  in 
this  bar,  —  the  subdivisions  of  the  yard  into  feet  being  traced  on 
the  plugs  in  the  middle  wells.  The  defining  end  lines,  which 
have  been  compared  with  the  British  Bronze  Yard  No.  11,  are 
the  middle  lines  of  the  groups  forming  short  chords  with  the  cir- 
cles marking  the  junction  of  the  gold  plugs  with  the  bronze. 
There  is  no  defining  cross  line.  The  settings  are  made  on  the 
middle  points  of  the  chords.  There  are  four  other  groups  of 
lines  on  this  bar,  but  they  have  not  been  used  in  these  compari- 
sons. The  appearance  of  the  tracings  is  as  follows  : 

Lines  on  gold  plug  of  bronze  yard  P.  and  W. 
No.  1. 

The  initial  point  of  measurement 
is  at  the  end  on  which  the  stamp 
P.  &  W.  No.  1  is  engraved. 

The  middle  line  of  group  marked*  is  the  initial 
FIG.   3.  point  of  measurement. 


25 

P.  &  W.  No.  2  is  a  bronze  bar  of  the  same  composition  as 
P.  &  W.  No.  1.  It  is  41  inches  long,  1  inch  wide,  and  1  inch 
deep.  Platinum-indium  plugs  are  inserted  in  the  bar,  as  shown 
in  the  following  sketch  : 


FIG.  4. 

ab  —  be  =  cd  =1  foot. 
aa!  —  a^  etc.,—  1  inch. 
deli  =  c^d  3  etc.,  Clinch. 
a  f  —  1  meter  at  62°  F. 

There  are  three  defining  lines  traced  on  each  plug.  The  com- 
parisons with  the  British  Bronze  Yard  No.  11  were  made  with 
the  middle  lines  on  plugs  a  and  d.  A  cross  line  at  right  angles 
to  the  tracings  runs  the  whole  length  of  the  bar.  The  point  a  is 
taken  as  the  initial  point  of  measurement. 

The  comparisons  were  made  on  the  "line  and  end  comparator," 
in  room  No.  6  of  the  Coast  and  Geodetic  Survey  Office.  The 
British  Yard  Bronze,  No.  11,  had  been  on  the  comparator  about 
two  weeks,  and  in  the  afternoon  of  January  21st  the  bar  P.  &  W. 
No.  1  was  also  placed  on  the  comparator.  On  January  22d  com- 
parisons wwe  made  by  Smith  alone,  and  on  January  24th  and 
25th  by  both  Rogers  and  Smith.  After  these  comparisons  were 
finished,  bar  P.  &  W.  No.  2  was  put  on  the  comparator  in  the 
place  of  P.  &  W.  No.  1,  and  compared  with  No.  11  on  January 
26th,  27th,  and  28th,  by  both  Rogers  and  Smith. 

In  this  comparator  the  microscopes  are  horizontal,  and  the  bars 
are  placed  with  the  defining  lines  vertical.  No.  11  was  supported 
at  its  neutral  points  upon  fixed  supports.  P.  &  W.  Nos.  1  and  2 
were  placed  upon  the  carriage  having  a  horizontal  motion  —  No. 

1  being  supported  at  points  seven  inches  from  each  end,  and  No. 

2  at  points  seven  inches  from  the  a  end  and  ten  and  a  half  inches 
from  the  f  end.     In  each  comparison  each  bar  was  in  position 
twice,  at  one  time  making  one  reading  and  at  the  other  two 
readings,  each  reading  being  the  mean  of  two  pointings,  so  that 
in  the  following  tables  of  results  each  result  is  the  mean  of  six 
pointings  at  each  end  of  each  bar.     Such  a  comparison  was  made 
in  from  ten  to  thirteen  minutes. 


26 


The  two  Fahrenheit  ("Green")  thermometers,  Nos.  9  and  12, 
were  used  —  No.  9  being  attached  to  the  British  Yard  Bronze 
No.  11,  and  No.  12  to  the  P.  &  W.  bar. 

The  corrections  to  these  thermometers  at  the  temperature  at 
which  the  comparisons  were  made  are  — 

No.    9=  4-0°.  03 
No.  12  =  +  0°.00 

On  the  following  pages  are  given  the  results  of  these 
comparisons : 

Results  of  comparisons  of  Bronze  Yard  P.  &  W.  No.  1  with  British  Yard 
Bronze  No.  11: 


Date. 


1881. 


January  22, 


January  24, 


January  25, 


Smith, 
Rogers, 


A.  M. 

9.35 

11.26 

P.M. 

1.18 
2.14 

A.M. 

9.30 
10.38 
11.51 

P.  M. 

1.21 
3.12 

A.  M. 

9.31 
11.09 

P.  M. 

1.12 

3.08 


Temp. 

F. 

DEGREES. 
62.45 
62.10 

61.60 
61.40 

57.10 
57.05 
56.90 

57.00 
57.10 

57.70 
57.55 

57.65 
57.70 
58.71 
57.33 


B.  Y.  B.  No.  11.      P.  &  W.  B.  No.  1. 


SMITH. 
INCH. 
-.000079 
120 

038 
120 

-.000190 
173 
151 

135 
227 

-.000163 
199 

168 

125 

-.000145 


ROGERS. 


—.000170 
087 

108 
209 

—.000170 
162 

098 
085 

—.000136 


Giving  Rogers'  result  two-thirds  weight,  we  have  — 

At  58°.  18  F.  No.  11  —  P.  &  W.  No.  1  =  —.000141  inch. 

*  Imperial  yard  -  No.  11  =  +.000088  inch. 

Imperial  yard  —  P.  &  W.  No.  1  =  —.000053  inch. 

*  Report  of  1877;  App.  No.  12,  page  5. 


27 


Results  of  comparisons  of  Bronze  Yard  P.  &  W.  No.  2  with  British  Yard 
Bronze  No.  11: 


Date. 

1881. 

A.  M. 

January  26, 

9.49 

11.21 

P.  M. 

1.28 

3.11 

A.  M. 

January  27, 

9.39 

11.24 

P.  M. 

1.23 

3.10 

A.  M. 

January  28, 

9.36 

11.22 

P.  M. 

12.36 

2.16 

Smith, 
Rogers, 


Temp. 

F. 

56.20 
56.16 

56.20 
56.35 

55.90 
55.55 

55.10 
54.60 

52.00 
51.75 

51.30 
51.30 
54.37 
54.98 


B.  Y.  B.  No.  11. 

SMITH. 

— ;  0001 16 

—.000114 

+.000004 
—  000060 

+  .000063 
—.000002 

—.000140 
—.000133 

—.000064 
—.000041 

—.000018 
+.000015 
—.000050 


P.  &  W.  B.  No.  2. 

ROGERS. 

—.000100 
—.000089 

+  .000022 
—.000084 

+.000052 
—.000014 

—.000125 
—.000098 

—.000072 
—.000041 


-.000055 


At  54°.70  F.  No.  11  —  P.  &  W.  No.  2  =  '—  .000052  inch. 

*  Imperial  yard  -  No.  11,  =  +.000088  inch. 

Imperial  yard  —  P.  &  W.  No.  2  =  +.000036  inch. 

*  Report  of  1877;  App.  No.  12,  page  5. 

Respectfully  yours, 

EDWIN  SMITH, 

Assistant  U.  S.  Coast  and  Greodetic  Survey. 

Report  approved, 

J.  E.  HILGARD, 

Assistant  in  Charge  Inspector  U.  S.  Standard  Weights  and  Measures. 


According  to  this  report,  P.  &  W.t  is  53  millionths  of  an  inch 
longer  than  the  Imperial  Yard,  and  P.  &  W.2  is  36  millionths  of 
an  inch  shorter  than  the  Imperial  Yard  at  62°. 0  Fahr.,  assuming 
that  "Bronze  11,"  P.  &  WBl  and  P.  &  W.a  have  the  same  coef- 
ficient of  expansion. 


28 

The  following  are  the  results  obtained  from  the  observations 
made  by  Mr.  Smith  and  myself  at  Washington,  with  my 
comparator  : 

Date.  Observer.  Temperature.  minus  P.  &  W.  i 


° 


Feb.  1,  R,  34.0  —0.000155  inch. 

1,  S.,  34.0  —0.000166 

4,  R.,  60.8  —0.000154 

6,  R.,  62.7  —0.000106 

7,  R.,  62.2  —0.000052 
Hence, 

P.  &  W.  j         —  0.000127  inch  =  "  Bronze  11." 

"  Bronze  11 "  +  0.000088  =  Imperial  Yard  =  Y. 

and 

P.  &W.j 

Date.  Observer. 

Feb.  1,  R, 

1,  R., 

1,  R-, 

1,  R., 

2,  R, 

2,  S., 

4,  R., 

7,  R, 

Hence, 

P.  &  W.2     -0.000027  inch  =  "Bronze  11." 
' '  Bronze  1 1"  +  0. 000088  =  Y. 

and 

P.  &  W.2  +  0.000061  inch  =  Y. 

Combining  these  results  and  assigning  equal  weights  to  each,  we  have  — 

0.000039 


—  0.000039  inch 

-vr 

Temperature. 

"Bronze  11," 
minus  P.  &  W.  2 

31.2 

—  0.000039 

inch. 

31.2 

4-  0.000028 

35.6 

—  0.000002 

35.6 

—  0.000083 

30.9 

—  0.000014 

30.9 

—  0.000030 

60.9 

—  0.000075 

62.2 

—  0.000059 

P.  &  W. ,    +     &000088  +_000006n 

L  2  J  • 

Or,  finally, 

P.  &  W.i  —0.000046  inch  =  Y. 
P.  &  W.8  +0.000048  inch  =  Y. 

Before  proceeding  with  the  discussion  of  the  comparisons  made 
subsequently  to  my  return  from  Washington,  the  details  of  the 
comparisons  of  the  Yard  C.  S.  with  the  Imperial  Yard  made  by 
Mr.  Chaney,  and  of  the  meter  C.  S.  with  the  Metre  des  Archives 
made  by  Dr.  Benoit  at  the  International  Bureau,  will  be  given. 


29 


The  following;  relations  for  the  Yard  are  taken  from  Mr.  Cha- 


ney's  report : 

Series. 

1 

2 

3 

4 

Whence, 


1  division  =  0.0000319  inch. 


Observer. 

Chaney, 
Rogers, 
Chaney, 
Rogers, 


Y  — C.  S. 

—  24.03  div. 

—  30.18 

—  26.96 

—  24.83 


Temperature. 

57°80 
58.25 
58.55 
58.65 


C.  S.  +0.00080  inch  =  Y. 

Or,  the  Coast  Survey  Yard  is  80  hundred-thousandths  of  an 
inch  too  short  at  62°.0  Fahr. 

The  following  are  the  equations  of  condition  formed  from  the 
comparisons  of  the  meter  C.  S.  with  Type  I  of  the  International 
Bureau,  quoted  from  the  report  of  Dr.  Fernet : 


No.  Obv's. 


C.  S.  minus 
Type  I. 


Weight. 


V. 


5  x+    1.2617  =  —  374. 52  p  1.5  +.1.17  p. 
4              aj+    1.2727  =  — 375.07  1.5  +0.52 

3              x+    1.2997  =  — 373.95  1.5  +1.39 

6  x+    1.4247  =  — 373.64  1.5  +0.57 

7  x  +    1.4907  =  — 373.56  1.5  +0.05 

17  x+    6.1547=— 331.52  1.0  —0.27 

14  x+   6.1577  =  — 330.02  1.0  +1.20 

18  x+    6.1617  =  — 331.76  1.0  —0.57 

19  x+   6.1707  =  — 332.11  1.0  —1.00 
13              x+   6.1887  =  — 333.40  1.0  —2.46 

15  x  +   6.1937  =  — 330.70  1.0  +0.20 

16  x+   6.2067  =  — 331.30  1.0  —0.52 

20  x+   6.2337  =  — 332.97  1.0  —1.43 
12              x+   6.2497  =  — 333.06  1.0  —2.67 
11              x+   6.2717  =  — 331.65  1.0  —1.46 
10              x+   6.3287  =  —  330.53  1.0  —0.86 

21  x+   6.3377  =  — 330.49  1.0  —0.90 
9              x+   6.4657  =  — 328.71  1.0  —0.28 

8  x+   6.4837  =  — 327.40  1.0  +0.86 
2              a? +  11.5647  =  —  279.97  1.0  +2.15 
1              x  + 11.9017  =  —276.41  1.0  +2.65 

Whence, 

C.  S.  —  Type  I  =  —  389.14^  ±  0.43// 

From  the  known  relation  between  Type  I,  and  the  Metre  des 
Archives  A,  the  following  relation  was  obtained  for  the  tempera- 
ture 0°  C.,  viz. : 

C.  S. +310.7//  =  A. 

The  coefficient  of  expansion  at  62°  =  17. 71  p  in  1  meter  for  each  degree 
Centigrade 


30 

The  meter  C.  S.  is  therefore  310.7  mikrons  too  short  at  32° 
Fahr. 

Employing  the  coefficient  determined  by  Benoit  in  the  reduc- 
tion from  32°.0  to  62°.0  Fahr.,  we  have  for  62°.0, 

C.  S.  +15.5/4=:  A. 
Or,  C.  S.  is  15.4  mikrons  too  short  at  62Q.0. 

The  following  are  the  relations  between  the  meter  T%  and  the 
Metre  des  Archives  A,  at  32°.0  and  62°.0  respectively : 

At  32°  At  62° 

T%  +  102.8//  =  A.  Tas  — 167.0,"  =  A. 

The  Tresca  meter  Tas  is  therefore  102.8  mikrons  too  short  at 
32°.0,  and  167.0  mikrons  too  long  at  62°.0. 

COMPARISON  BETWEEN  METEKS  T  AND  P.  &  W.2a2. 

Two  series  of  comparisons  between  these  standards  were  insti- 
tuted, one  Aeries  with  Comparator  No.  1,  and  the  other  with  the 
Universal  Comparator.  In  the  iirst  series  two  microscopes 
attached  to  the  carriage  were  used.  The  bars  were  placed  at  a 
distance  2  x  centimeters  apart,  and  observations  were  made  for 
the  positions  -f  x  and  —  x. 

For  x  =  +  3.0  cm. 

At  62°.  0  F. 

T«8— P.  &  W.8a2. 

+  164.0/Z 
+  163.8 
+  159.2 
+  158.5 
+  166.9 
+  159.6 
+  153.3 
+  150.0 
+  152.5 
+  152.3 
+  165.2 
+  163.7 
+  161.7 
+  158.8 
+  159.7 
+  160.5 
+  161.1 
+  162.6 


Date. 

1881. 

(r—  62°.0)F. 

Ta2  —  P.  &  W.s' 

Feb.  14 

+  24.1 

+  177.  7  ti 

15 

+  23.5 

+  177.2 

16 

—  12.2 

+  152.2 

17 

--13.  2 

+  151.0 

20 

+  32.5 

+  185.4 

21 

+  22.2 

+  172.2 

22 

—  13.7 

+  145.5 

23 

—  13.7 

+  142.8 

Mar.  16 

—  8.9 

+  147.5 

23 

—  13.6 

+  144.6 

24 

—  9.7 

+  154.0 

25 

+  26.8 

+  178.9 

29 

—  11.8 

+  155.0 

30 

—  13.2 

+  151.3 

31 

-15.4 

+  151.0 

Apr.    3 

+  29.3 

+  187.2 

8 

+   6.9 

+  165.0 

10 

+   8:9 

+  167.6 

Feb.  24 
25 

Mar.  11 
13 
14 
15 
16 


—16.3 
+35.9 
+  4.8 
+23.1 
+19.6 
+22.4 
—  9.0 


31 

For  #=  —  3.0  cm. 

+  165. 5  p 
+  197.8 
+  174.7 
+  183.6 
+  186.1 
+  189.3 
+  163.2 


+  177.4 
+  172.0 
+  170.5 
+  175.3 
+  176.6 
+  163.7 


We  have,  therefore, 


—  R' 


For  x  =  +  3.0  cm.  =  +  159.7  p. 

X—  —  3.0  cm.  =  +  172.9  p. 

Mean  =  +  166.3  p. 

With  the  Universal  Comparator. 

EQUATIONS  OF  CONDITION  BETWEEN  Ta2  AND  P.  &  W.3aa 

(With  1-inch  objective.) 

1  div.  =  0.440  u 


Date. 

1882. 

Ta2—  P.  &  W.2 

Apr.  26 

+  401.  5  div. 

27 

+  396.8 

28 

+  391.7 

30 

+  392.3 

May    3 

+  393.9 

12 

+  380.0 

20 

+  372.8 

23 

+  375.2 

At  62°  F. 

(r—  62°)F. 

Ta2—  P.&W.2a2. 

No.  Obs. 

a  —16.306 

+  380.1  div. 

3 

a  —13.41  6 

+  379.2 

4 

a  —12.156 

+  375.8 

5 

a  —10.476 

+  378.6 

5 

a  —  9.426 

+  381.6 

5 

a  —  1.246 

+  378.4 

3 

a  +   2.98  6 

+  376.7 

3 

a  +   4.646 

+  381.3 

3 

Normal  Equations. 

+  3104.2=+   8. 00  a—  55.376    Whence,  6  =  -      1.31  div.  =  —  0.58  p 
—  22062.0  =  —  55.37  a  +823.306    Whence,  a  =+  378.9  div.  =  +  166.0  p 

Combining  the  results  obtained  from  the  two  comparators,  we 
find: 

Ta2--P   &  W  82  _  1 66.3  p  +  166.0  p_ 

"2  c\  '      j* 

Since  Ta2  —  167.°^=  A. 
We  have : 


Or: 


p.  &  W.2a2  —  0.9  n  =  A. 


Meter  P.  &  W.2a2  is  0.9  mikron  too  long  at  62°.0  Fahr. 


S2 

A  more  extended  series  of  comparisons  between  between  Tas, 
C.  S.,  and  P.  &  W.2*2,  and  also  the  steel  standard  Iin  both  for 
meter  and  the  yard,  was  made  in  1883.  The  details  are  given 
on  pp.  362-371,  proceedings  of  the  American  Academy.  Only 
the  results  for  the  normal  temperatures  0°  C.  and  16°. 67  C.  are 
given  here.  The  columns  A,  represent  the  deviations  of  the 
observed  relations  from  the  mean  value  derived  from  the  entire 
series. 


33 


COMPARISON  OF  METERS  Ta2.  T'-i,  R^,  R^s,  AND  YARDS 


Date. 

Y  61 

.0 

'—  ** 

y 

A 

A 

M 

«si 
i  u 
rs 
aS 

A 

A 

M 

fe 

I* 

pf 

A 

A 

1883. 
March  22  

0 

—  1.93 
—  1.30 
—  0.25 
+  2.27 
+  0.921 
+  6.401 
+  1.05! 
—  0.381 
+  1.25 
+  0.07 
—  0.14 
+  4.51 
+  12.58 
+10.34 
+  6.98 
+  14.68 
+14.58 
+  15.02 
+14.75 
+1446 
+  1454 
+14.43 
+14.66 
+  14.84 
+  14.58 
+  14.49 
+  14.27 
+  14.41 
+  1464 
+  14.76 
+14.79 
+  14.80 
+  14.99 
+19.18 
+  17.59 
+  17.07 
+  17.07 
+  17.23 
+  17.8(5 
+  17.89 
+  18.04 
+  17.87 
+  17.97 
+  18.1(5 
+  18.03 

r.  26... 
nl    1... 
r.   10... 

y  18... 
y  23... 
y   29... 
le    4.  .  . 
le  26.  .  . 
le  28.  .  . 

div. 
-13.8 
—13.6 
—15.8 
-15.5 
—14.1 
—13.1 
—15.4 
—15.2 
—13.3 
—15.6 
-14.9 
—14.8 
—13.8 
14  1 

div. 
+1.8 
+2.0 
-0.2 
+0.1 
+  1.5 
+2.5 
+0.2 
+  0.4 
+2.3 
0.0 
+  0.7 
+  0.8 
+  1.8 
+  1.5 
+3.0 
+2.0 
—1.0 
+  1.3 
-1.7 
—0.3 
+0.6 
—0.7 
—0.8 
—1.0 
—1.2 
—1.5 
+0.4 
—2.8 
-2.1 
-2.4 
—1.1 
—1.1 
—1.1 
—0.4 
—0.6 
+0.6 
—0.5 
-1.7 
i—  14 
—0.9 
+0.5 
+  1.7 
+  1.0 
—1.0 
—2.4 

+  1.05 
1+1.09 
+1.5? 
+0.17 
—0.61 
—1.64 
—0.85 
—0.77 
—  0.03 

P 

+0.8 
+0.9 
—0.1 
+0.0 
+0.7 
+  1.1 
+01 
+0.2 
+  1.0 
+0.0 
+0.3 
+  0.4 
+0.8 
+0.7 
+  1.3 
+0.9 
—04 
+0.6 
—0.7 
—01 
+0.3 

—0:3 

-04 
—0.4 
—0.5 
—0.7 
+0.3 
—1.2 
—0.9 
—1.1 
—0.5 
—0.5 
—0.5 
-02 
-0.3 
+0.3 
—0.2 
—0.7 
—0.6 
—0.4 
i+0.2 
+0.7 
+0.4 
—0.4 
—1.1 

+0.46 
:  +  0.48 
+0.51 
+0.07 
!—  0.27 
—0.72 
—0.37 
—0.35 
—0.01 

div. 

div. 

/" 

div. 

div. 

P 

23  
25  ! 
25  
26  











28 

29  ... 

30  
30  .... 
April      1  
2  ... 



;:;;;; 









3  

8 

9 

10     ... 

—12.6 
—13.6 
—16.6 
—14.3 
—17.3 
—15.9 
—15.0 
—16.3 
—16.4 
—16.6 
—16.8 
—17.1 
—15.2 
—18.4 
—17.7 
—18.0 
—16.7 
—16.7 
—16.7 
—16.0 
—16.2 
—15.0 
—16.1 
—17.3 
—17.0 
—16.5 
—15.1 
—13.9 
—14.6 
-16.6 
—18.0 

—14.56 
—14.52 
—14.04 
—15.44 
—16.22 
—17.25 
—164(3 
—  16.3S 
—15.64 

May     14  

—9.8 
—7.2 
—58 
-8.4 
—6.7 
—8.0 
—7.8 
-97 
—8.9 
—8.7 
—8.0 
—8.2 
-7.7 
—8.4 
—7.3 
-8.9 
—8.7 
—9.7 
—6.7 
—7.6 
—6.3 
—8.7 
-6.5 
—7.7 
—9.5 
—7.1 
—6.7 
-8.4 
-9.9 
—7.9 
i 

—1.8 
+0.8 
+2.2 
—0.4 
+1.3 
0.0 
+0.2 
—1.7 
—0.9 
—0.7 
0.0 
—0.2 
+0.3 
—0.4 
+0.7 
-0.9 
—0.7 
—1.7 
+1.3 
+0.4 
+  1.7 
—0.7 
+1.5 
+03 
—1.5 
+0.9 
+1.3 
—0.4 
—1.9 
+0.1 

-0.8 
+0.3 
+1.0 
—0.2 
+06 
+0.0 
+0.1 
—0.7 
—0.4 
—0.3 
+00 
—0.1 
+0.1 
—0.2 
+0.3 
—04 
—0.3 
—0.7 
+0.6 
+0.2 
—0.7 
—0.3 
+0.7 
+0.1 
—0.7 
+0.4 
+0.6 
—0.2 
-0.8 
+  0.0 

15  

+0.1 
—2.0 
—  1.1 
—1.1 
+0.6 
—21 
—1.6 
—1.2 
—2.2 
—1.0 
—1.4 
—1.2 
—2.2 
—2.7 
—23 
—0.6 
-2.9 
—3.5 
—1.7 
—15 
0.0 
—0.2 
0.0 
—1.0 
—2.0 
-2.0 
—3.1 
+  1.0 
+2.1 

+  1.4 

—0.7 
+0.2 
+0.2 
+1.9 
-0.8 
—0.3 
+  0.1 
—0.9 
+0.3 
—0.1 
+0.1 
-0.9 
—1.4 
—1.0 
+0.7 
—1.6 
—2.2 
—0.4 
—02 
+  1.3 
+  1.1 
+  1  3 
+0.3 
—0.7 
—0.7 
—1.8 
+2.3 
+3.4 

+0.6 
—0.3 
+0.1 
+0.1 
+0.8 
—0.4 
—0.1 
+0.0 
-0.4 
+0.1 
+0.0 
+0.1 
—0.4 
-0.6 
—0.4 
+0  3 
-0.7 
—1.0 
-0.2 
—0.1 
+06 
+0.5 
+0.6 
1+0  1 
-0.3 
-0.3 
—0.8 
+  1  0 
+  1.5 

16 

17  
18  

19  

20 

21   ... 

22  

23  
24 

25  

27  .... 

28  

29  
30 

31  
June      1  
3 

4  
5 

6  

7 

25  
26  

26  
27  

27  
27  

28  

Mar.  22  to  Ma 
Mar.  28  to  Ap 
Apr.    2  to  Ap 
May  14  to  Ma 
May  19  to  Ma 
May  24  to  Ma 
May  30  to  Jui 
Juue    5  to  Jui 
June  26  to  Jui 

—7!  58 
—8.62 
—7.92 
1—8.32 

i—  7.74 
—  8.0C 

+CK45 
—0.59 
+0.11 
—  02fl 
I+0.2H 
1+0.03 

+0.20 
—0.26 
+0.05 
—01: 
+O.lb 
+0.01 

—  1.  02  +0.24+0.  ii 
—  1.30J—  0.04—  0.01 
—1.70—044-0.19 
—2.20—  0.94'-  041 
—0.541+0.72  +0.32 
—  0.80+0.  46i+  0.20 

MEANS  

-15.61  =—6.87  /*    —  8.03  =  —  3.53/u    —  1.26  =  —  O.oo// 

34 


COMPARISON 


OF  METERS  C.  S., 
At  0°  and  at  16°.  67. 


AND  P.  &  W2 


Date. 

r 

91 

fl 

P? 
I 

QQ 

d 

« 

sTo 
1* 

*3 

O 

A 

A 

0) 

a 

£ 

<3 

Pk 

OQ 

d 

M 
08 
« 

£ 

^d 

ft 

cd<1 
d 

A 

A 

1883. 

o 

div. 

div. 

div. 

(• 

div. 

div. 

div. 

f* 

Mar.  22 

—  1.93 

—  350.4 

-317.9 

—  0.3 

—  0.1 

—  56.9  —55.4 

+    2.2 

+  10 

23 

—   1.30 

—  337.2 

—  315.3 

+   2.3 

+  1.0  —54.9  —53.9 

+   3.7 

+  1.6 

25 

—   0.25 

—  323.4 

—  319.2 

—   1.6 

—  0.7 

—  54.3  _54.2 

+    3.4 

+  15 

25 

+   2.27 

—  288.0  —326.2  —  8.6 

-8.8 

—  58.5 

—  60.2 

—  2.6 

—  1.1 

26 

+    0.92 

—  308.0 

—  323.51  —  5.9  —2.6 

—  58.7 

—  59.4  —   1.8 

—  0.8 

98 

+   6.40 

—  204.7 

—  312.5 

+    5.1  +2.2 

—  48.3 

—  53.1   +    4.5 

+  2.0 

29 

+    1.05 

—  302.2 

—  319.9 

—  2.3  —1.0 

—  57.7 

—  58.5  —  0.9 

—  0.4 

30 

—  0.38  —3246 

—  318.2 

—  0.6 

—  0.3  —5(5.7 

—  56.3 

+    1.3 

+  0.6 

30 

+    1.25  -  290.7 

—  311.8 

+    5.8 

+  3.8  —54.3 

—  55.2 

+    2.4 

+  1.0 

Apr.    1 

+   0.07!—  311.3 

—  312.5 

+    5.1 

+  2.2 

—  58.3 

—  58.4 

—  0.8 

—  0.4 

2 

—  0.14 

—  323.9  —321.6 

—  4.0 

—  1.8 

—  65.0 

_64.9  —  7.3 

—  3.2 

3 

+    4.51 

—  243.21  —319.2 

—  1.6 

—  0.7 

—  56.6 

—  60.0  —  2.4 

—  1.1 

8 

+  12.58 

—  106.1 

—  318.1 

—  0.3 

—  0.1 

—  48.6  —58.2 

—   0.6 

—  0.3 

9 

+  10.34 

—  140.4  —314.6 

+    3.0 

+  1.3 

—  50.4  —58.2 

—   0.6 

—  0.3 

10 

+    6.98 

—  195.6!  —313.2 

+    4.4 

+  1.9 

—  52.9  —58.1 

—   0.5 

—  0.2 

At  16°.67 

At  16*67 

May  14 

+  14.68  —  71.9 

—   38.4 

—  6.3 

—  2.8 

—  38.2 

—  36.7    f    5.9 

+  2.6 

15 

+  14.58—  66.5 

—   31.3 

+   0.8 

+  0.4 

_45  2  —43.6  —   1.0 

—  0.4 

16 

+  15  02i  —  53.4 

—  25.6 

+    6.5 

+  2.9 

—  33.  bj—  32.4  +10.2 

+  4.5 

17 

+  14.75!  —  62.3 

—   29.9 

+   2.2 

+  1.0 

—  44.5!  —  43.01  —   0.4 

—  02 

18 

+  14.46 

—   57.1 

—   19.9 

+  12.2 

+  5.4 

—  44.4  —42.8  —   0.2|—  0.1 

19 

+  1454 

—  70.4  —  34.5 

—  2.4—1.1 

—  42.5  —40.  9!  +    1.7 

+  0.7 

20 

+  14.43  —   68.3  —   30.6 

+    1.5 

+  0.7 

—  40.3  —38.7   +    3.9 

+  1.7 

21 

-t-  14.66  —  66.6  —   32.7 

—  0.6 

—  0.3 

—  43.5 

—  42.0  +    O.G 

+  0.3 

22 

+  14.84  —   63.2 

—   32.4 

—  0.3 

—  0.1 

—  41.9 

—  40.5  +    2.1 

+  0.9 

23 

+  14.58  —   67.5 

—   32.3 

—  0.2 

—  0.1 

—  38.1 

—  36.5 

+    6.1 

+  2.7 

24 

+  14.49 

—  75.3 

—  38.6 

—  6.5 

—  2.9 

—  46.3 

—  44.7 

—  2.1 

—  0.9 

25 

+  14.27 

—  73.1 

—  32.7 

—  0.6 

—  0.3 

—  43.3 

—  41.5  +    1.1 

+  0.5 

27 

+  14.41 

—  72.0 

—   33.9 

—  1.8 

—  0.8  —41.8 

—  40.1   -f    2.5 

+  1.1 

28 

+  14.64 

—  70.7 

—  36.5 

—  4.4 

—  1.9  —45.3 

—  43.8  —   1.2 

—  0.5 

29 

+  14.76 

—  68.5 

—  36.3 

—  4.2 

—  1.8 

_44.9  _42.6  —   0.3 

—  0.1 

30 

+  14.79 

—  63.9 

—  32.3 

—   0.2 

—  0.1 

—  41.6 

—  40.2  +    2.4 

+  1.1 

31 

+  14.80;  —  67.4 

—  359 

—  3.8 

—  1.7 

—  42.4 

—  41.0  +    1.6 

+  0.7 

June   I 

+  14  99  —  60.8i  —  32.5 

—   0.4 

—  0.2 

—  41.9 

—  40.7  +    1.9 

+  0.7 

3 

+  19.18  +    11.8  —   30.5 

+    1.6 

+  0.7 

—  40.7 

—  42.6  +    0.0 

+  0.0 

4 

+  17.59  —  19.0 

—  34.5 

—   2.4 

—  1.1 

—  37.7 

—  38.4  +    4.2 

+  1.8 

5 

+  17.07 

—   22.9 

—  29.6 

+   25 

+  1.1 

—  37.7 

—  38.0  +46 

+  2.0 

6 

+  17.07|—  20.2 

—  26.9 

+   5.2  +2.3  —42.7 

_43.0  _  0.4 

—  0.2 

7 

+  17.231  —   19.2  —  28.7 

+   3.4  +1.5 

_  4i.6i—  42.1    +    0.5 

+  0.2 

25 

+  17  80  —   15.8  —   35.8  —   3.7  —1.6 

—  45.0  —45.8:—  3.2 

—  1.4 

26 

+  17.89  —   10.2  —   30.4 

+    1.7  +0.71—44.3  —44.1  —  1.5 

—  0.7 

26 

+  18.04  —  11.  Oj—   34.2 

—  2.1  —0.9 

—  43.6  —50.9!—  8.3 

—  3.7 

27 
27 
27 

+  17.87 
+  17.97 
+  18.10 

—   ll.fc 
—     8.0 
—     4.8 

—   31.6 
—   30.0 
—   29.5 

+   0.5 
+   2.1 
+   2.6 

+  0.2 
+  0.9 
4-1.1 

—  42.5 
—  44.7 
—  41.6 

—  48.9!—  63 
—  51.7  —  9.1 
—  49.5  —  69 

—  28 
—  40 
—  31 

28 

+  is.oa  —  11.1 

—  34.0  —   1.9  —0.8!  —43.4 

—  50.61—  8.0 

—  04 

35 


COMPARISON  OF  METERS  Rj  AND  R2,  AND  OF  YARDS  R±  AND  R2. 

At  0°  and  at  16°. 67. 


Meters. 

Yards. 

0 
Si 

*« 

OS 

91 

Date. 

T 

1 

fe 

A 

A 

| 

•$? 

A 

A- 

PH' 

P-I  ° 

PLJ 

PH  ° 

i 

1  <ri 

1 

|  ^ 

01 

ej 

a 

oS 

a 

P? 

P? 

p? 

P? 

1883. 

o 

div. 

u 

div. 

^ 

Mar.  22 

—  1.88J  +293.5 

+262.5 

+  2.5 

+  1.1 

+269.1 

+240.4 

—9.8 

—4.3 

23 

—  1.30 

+282.3 

+261.4 

+  1.4 

+0.6 

+268.4 

+248.9 

—1.3 

—0.6 

25 

—  0.25 

+269.1 

+264.9 

+  4.9 

+2.2 

+253.7 

+244.  1 

—6.1 

—2.7 

25  +  2.27 

+229.5 

+266.0 

+  6.0 

+2.6 

+225.2 

+251.1 

+0.9 

+0.4 

26+  0.92 

+249.3 

+264.1 

+  4.1 

+  1.8 

+239.9 

+253.6 

+3.4 

+  1.5 

28!+  6.40 

+156.4 

+259.4 

—  0.4 

—0.2 

+  1846 

+249.8 

—0.4 

—0.2 

29!+  1.05  +244.5 

+261.4 

+  1.4 

+06 

+237.8 

+253.4 

+3.2 

+  1.5 

30 

—  0.38  +267.9 

+261.9 

+  1.9 

+0.8 

+259.1 

+253.5 

+  3.3 

+  1.5 

30 

+  1.25!  +236.4 

+256.6 

—  3.4 

—1.5 

+229.4 

+248.0 

—2.2 

—1.0 

Apr.    1 

+  0.07 

+253.0 

+  254.1 

—  5.9 

—2.6 

+249.2 

+250.3 

+0.1 

+0.0 

2—  0.14 

+258.9 

+256.7 

—  3.3 

—1.5 

+250.  1 

+247.9 

—2.3 

—1.0 

3  +  4  51 

+  186.6 

+  259.2 

—  0.8 

—0.4 

+  185.3 

+252.3 

+2.1 

+0.9 

8 

+  12.58  +  57.5 

+259.9 

—  0.1 

+0.0 

+  64.9 

+251.8 

+  1.6 

+0.7 

9 

+  10.34  +  90.0 

+256.4 

—  3.6    —1.6 

+  99.9 

+253.8 

+3.6 

+  1.6 

10 

+  6.98  +142.7 

+255.1 

—  4.9    —2.2 

+  150.2 

+254.1 

+3.9 

+  1.7 

At  16°.  67 

At  16°  .67 

May  14 

f!4.68[+  33.7][+     1.7]  +   .      [+0.71 

+  36.9 

+     7.3 

+3.4 

+  1.5 

15  +  14.58;  +  21.3    —  12.3 

—  1.8    —0.6 

+  30.4 

—    0.7 

—46 

—2.0 

16 

-j-15.02  +  19.8 

—     6.8 

+  4.2 

+  1.8 

+  32.2 

+     7.6 

+3.7 

+  1.7 

17+14.75!  +  17.8 

—  13.1 

—  2.1 

—0.9 

+  30.0 

+     1.4 

—2.5 

—1.1 

18+14.46j  +  12.7 

—  22.9 

[—11.  9]  [—5.2; 

+  28.1 

—    4.8 

[—8.7] 

-3.8] 

19 

^14.54 

+  27.9 

—    6.4 

+  4.6 

+2.0 

+  34.6 

+     2.9 

—1.0 

—0.4 

20 

+  14.43  +  28.0 

—    8.1 

+  2.9 

+  1.3 

+  36.0 

+     2.7 

—1.2 

—05 

21 

-f-14.66  +  23.1 

—    9.3 

+  1.7 

+0.7 

+  31.2 

+     1.3 

—2.6 

—1.1 

22 

f  14.84  +  21.3 

—    8.1 

+  2.9 

+  1.3 

+  36.2 

+     9.0 

+5.1 

+2.2 

23 

T  14.58  +  29.4 

—    4.2 

+  6.8 

+3.0 

+  30.0 

—    1.0 

-4.9 

—2.2 

24 

4-1449  +  29.0 

—    6.1 

+  4.9 

+2.2 

+  39.3 

+     6.9 

+3.0 

+  13 

25  +  14.27 

+  29.8 

—    8.8 

+  2.2 

+0.9 

+  31).  3 

+     3.6 

—0.3 

—0.1 

27 

+  14.41 

+  30.2 

—    6.2 

+  4.8 

+21 

+  37.9 

+     4.3 

+0.4 

+0.2 

28+14.64)  +  25.4 

—    7.3 

+  3.7 

+  1.6 

+  40.6 

+  10.4 

+6.5 

+2.9 

29+14.76  +  24.2 

—    6.6 

+  4.4 

+  1.9 

+  30.1 

+     1.7 

—2.2 

—1.0 

30+14.79  +  22.3 

—    7.9 

+  3.1 

+1.4 

+  33.3  +     5.2 

+  1.3 

+0.6 

31  +14.  SO  +  25.0 

—    5.1 

+  59 

+2.6 

+  32.9  +     5.0 

+  1.1 

+0.5 

June  1+14.99  +  18.9 
3+19.18  —  52.5 

—    8.2 
-  12.1 

+  2.8 
—  1.1 

+  1.2 
—0.5 

+  30.3  +     5.2 
+  37.1  +     0.3 

+  1.3 
—3.6 

+  0.6 
—  1  6 

4+17.59 

—  18.7 

—    3.9 

+  7.1    +3.1 

-    8.1 

+     5.6 

+  1.7 

+0.7 

5+17.07  —  14.8 

—    8.4 

+  2.6 

+  1.1 

-    3.9  +     21 

—1.8    —0.8 

6+17.07  —  22.5 

—  16.1 

—  5.1 

—2.2 

+     0.2  +     6.2 

+2.3 

+  1.0 

7+17.23:  —  22.4 

—  13.4 

—  2.4 

—1.1 

-    4.9  +     04 

—0.5 

—0.2 

251+17.86  —  29.2 

—  10.0 

+  1.0 

+0.4 

-  17.1  +     3.5 

—3.4 

—1.5 

26+17.89  —  34.1 

—  13.7 

27 

—1.2 

-  14.0  +     3.9 

0.0 

+0.0 

264  18.04  —  32.6 

—  16.7 

—  5.7 

—2.3 

-  13.5  +     6.8 

+2.9 

+  1.3 

27+17.8?  —  31.2 

—  17.3 

—  6,3 

—2.8  - 

-16.1  +     1.8 

__o  1    _0.9 

27+17.97j—  36.7    —  21.7 

—10.7 

—4.7  - 

-19.1   +     0.2 

—3.7 

—1.6 

87+18.16!—  36.7  |—  20.0 

—  9.0 

—4.0  - 

-  16.8!  +     5.4 

+1.5 

+0.7 

28+18.031  —  32.3 

—  16.6 

_  5.6    —5.5  - 

-  17.1!  +     3.2 

_07    —03 

COLLECTION  OF  RESULTS  IN  GROUPS  OF  FIVE  DATES  EACH. 

Meters. 
At  0°  C. 


T*a-C.S. 

div. 

+  474.2 
+  472.0 
4  473.5 

Means +  473. 2 


+  419.0 
+  418.1 
+  419.3 
+  417.1 
+  419.8 
+  420.9 

Means  +419.0 


Ta2-R1as  Ta2-P.&W.2a2  C.S.-R^s 

div. 

div. 

div. 

+  153.8 

+  417.6 

—  320.4 

+  157.0 

+  415.7 

—  315.0 

+  156.1 

+  413.6 

—  317.4 

+  155.6 

+  415.6 

—  317.6 

At  16 

°.67  C. 

+  389.9 

+  379.8 

—  29.1 

+  385.6 

+  378.4 

—  32.5 

+  383.7 

+  376.7 

—  35.6 

+  384.0 

+  376.5 

—  33.1 

+  389.5 

+  377.2 

—  30.3 

+  389.0 

+  370.5 

—  31.9 

+  386.9 

+  376.4 

—  32.1 

C.S.-P.&W.2*2 
div. 

—  56.6 

—  56.3 

—  59.9 


57.6 


—  39.7 

—  39.7 

—  42.6 

—  40.6 

—  42.6 

—  50.4 

—  42.6 


div. 
+  263.8 

+  258.7 

+  257.5 

+  260.0 


—  10.6 

—  7.2 

—  7.0 

—  7.5 

—  12.3 

—  18.5 


—  10.5 


Whence  the  following  relative  coefficients  are  derived :  — 
_L  473. 2  — 419.0 


For  T  — C.  S. 


T  — 


16.67 


.=   +3.25  =  + 1.43 


. 
b= 


+  155.6  —  386.9 
16.67 


-—  13.87=—  6.10 


T_P.&W. 


C.S.  — R! 


16.67 


^-317.6  +  32.1    =_1?.12=_ 


16.67 


C.S.-P.&W..  s=-57:!±42-6  =  -o.9o=-o. 


16.67 


40 


Ri_P.&W. 


16.67 


Converting  b  for  C.  S.— E1?  C.  S.— P.&W.2,  and  Ej— P.&W. 
into  the  equivalent  values  for  1  yard,  we  have 

For     C.  S.  — R  £=—6.91 


C.S.  —  P.&W. 


I  —  —0.36  yu 
5=_|_6.54^ 


37 


C.S.—  IV2 

div. 

—  307.5 

—  307.5 

—  310.5 


Means— 308.5 


Means  —  52.7 

Hence :  — 
For  C.  S.  — R 


Yards. 

At  0°  C. 
c.  a— P.&WV 

div. 

—  60.0 

—  56.5 

—  58.5 

—  58.3 


—  49.1 


-308.5       52.7 


—  P.&W.2aa 

div. 

+  247.5 
+  251.0 
+  252.0 


+  250.2 


+  2.2 
+  2.9 
+  5.4 
+  4.3 
+  3.2 
+  3.4 

+  3.6 


_ 
—15.35—6.75 


as.— P.&W.O  ft  = 


,  —58.3    +49.1 


16.67 


16.67 


=  —0.55=— 0.24 


i  =  -1-6.51 


Converting  these  values  into  the  equivalent  values  for  1  meter, 

we  have 

For     C.S.  — Rj  ft  =—  7.38 /z 

C.S.— P.&W.2        5=— 0.27/i 
Rj—  P.&W.2        6=+7.12  p 


Combining  these  results,  we  have 

For  1  Meter. 
For     T  — C.S.  ft=+1.43,i 

T  — R1  ft=— e.lOju 

T  — P.&W.3         ft  =+1.03,i 
as.  —  Rj  ft=— 7.46/i 

as.— p.&w.2  ft  =—0.33^ 

Rj— P.&W.3      ft  =+7.13^ 


For  1  Yard, 
ft  =+1.31,1 

ft  =— .  5.58^ 
I  =+0.94^ 
ft  =—6.83  fji 
ft  =—0.30^ 
ft  =+6.52^ 


.38 

The  following  relations  result  from  the  discussion   of  these 
observations :  — 

Adopted  Relations  for  the  Meter. 

At  0°  C.     At  16°.67  C. 
T-2    — C.  S.  —  +208.3  /i     =  4-184.6/1 

Ta2    —  R/a  =+    68.4/1     =+  170.2  /z 

Ta2    --P.  &  W.2a2=+  182.1  /i     =-{-165.5/1 
C.S.  — R/2  =— 139.7  /i     =—    14.1  /i 

C.  S.  —  P.  &  W.aa2  =—    24.8 /z     =_    17.7/1 
R/2  — P.  &  W.2a2  =4- 114.4/1     =—      4.6/1 

Adopted  Relations  for  the  Yard. 

At  32°.0  Fahr.  At  62°.0  Fahr. 
C.S.— R/2  =—135.7/i     =—    23.2/1 

C.  S.  —  P.  &  W.2«2  =—   25.6/1     =—    21.6/1 
R/2  — P.  &  W.2a2=:-f]10.1/i     =4-      1.6/i 

With  the  already  determined  coefficients  16.18  /i  and  17.60  /i 
for  T  and  C.  S.  respectively,  we  have : 

At  0°  C.  Ta2    4-  102.8  /i  =  A 

But  at  0°  C.  8.4-  310. 7  /i  =  A 

Hence,  Ta2   —  C.  S.   ;i  =  4- .207.9/1 

From  observations,  Ta2    — C.  S.    /i  =  4-  208.3 

Difference  =  0.4  /i 

At  16°.67  C.  Ta2    —167. 0 /i  =  A 

C.  S.  4-    15.4  /i  =  A 

Hence,  Ta3    —  C.  S.    /z  =  4-  182.4  /i 

From  observations,   Ta2    — C.  S.    /i  =  4-  184.6  /i 

Difference  =  2.2  /i 

We  have  therefore  an  agreement  between  the  different  results 
quite  as  close  as  one  ought  to  expect. 

For  the  yard  we  have  from  the  observations  at  Washington 

At  62°.0  Fahr. :  P.  &  W.  2'2  4-  1.22  /i  =  Y 
From  the  report  of  Mr.  Chaney: 

C.  S.  4- 20.32 /i  =Y 

Hence,  C.  S.  —  P.  &  W.  2a2         =  —  1 9. 1  /i 

Fr.om  observations,  C.  S.  —  P.  &  W.2'2         =  —  21.6  /i 
Difference  =  2.5    . 


39 


With  Peirce's  relation  between  "  Bronze  11 "  and  Y,  this  dif- 
ference is  reduced  to  0.0  p 

We  have  finally : 

For  the  Meter. 

At  0°  G.  At  16°.67  C. 

T*2  — A  =—102.8^  Ta2  — A 


=      182.1 


A     =—171.2^ 


But 

Ta2  — R 
Ta2— P. 

Whence: 

R/2 

P.  &  W./2- A  =—284.9  p 

Also, 
C.S.  — A  =  —  310.7 /* 

But 

C.S.  — R/2          =—139.7  p 
C.S.— P.&W.2a2=:—    24.8  p 

Whence: 

R/2  — A  =—171.0,1 

R2a2— A  =—  285.9  p 

By  combination  we  have: 

At  0°  C. 

Bi»3  -j-  171.1  p  —  A 

P.  &  W.2a2-f  285.4  p  =  A 


But 

Ta2— P.2&  } 
Whence: 
R/a  —  A 
R2a2  — A 

Also, 

C.S.  — A 

But 

C.  S.  —  R/a 


=  +167.0^ 

=  +  170.2  p 
=  +165.5  p 

=—      3.2  p 
=+      1.5  ^ 

=—    15.4  ju 
-    H.I 


C.  S.  —  P.&W.2a2=—    17.7 


Whence: 


—A     =—       1.3 

2.3 


P.  &W.2a2—  A     = 


At  16°.67  C. 
P/&  W.2a2—  1.9  p  =  A 


Collecting  our  results  for  Meter  P.  &  W./2,  we  have  for 
16°.6T  C.  =  62°.0  Fahr. : 

From  comparisons  with  the  Tre?ca  Meter  in  1881,  P.  &  W.  2n2  —  1  5  //  =  A. 

From  comparisons  with  the  Tresca  Meter  in  1883,  P.  &  W.  2!V2  —  0.9  /u  —  A 

From  comparisons  with  the  Meter  C.  S.  [Rogers],  P.  &  W.2a2  —  2.3  /a  =  A. 

From  comparisons  with  the  Meter  C.  S.  [Benoit],  P.  &  W.  2a2  —  2.3  p  =  A 


And  finally 
Or; 


P.  &  W.2a2  —  1.8  p  =  A. 


P  &  W.2tt2  is  1.8  mikrons  too  long  at  16°.67  C. 


40 

For  the  Yard. 

Adopting  for  the  relations  between  "  Bronze  11 "  and  Y,  the 
mean  of  the  values  found  by  Hilgard  and  Peirce,  viz.,  0.000055 
in.,  we  have: 

Smith  -f  Rogers,         P.  &  W.2a2  —  0.000007  in.  =  Y 

2 

Chaney,  C.  S.  -f  0.000800  in.  =Y 

From  comparisons,      C.  S.  +  0.000851  in.  =P.  &  W.2a2 

Whence:  P.  &  W.  "2  —  0.000051  in.=Y 


And  finally,  adopting  the  mean  relation  : 
Or: 


P.  &  W.2-2— 0.000029  in.=Y 


The  Yard  P.  &  W.2a2  is  29  millionths  of  an  inch  too  long  at 
62°.0  Fahr. 

Investigation  of  the    Yard  and  Meter  P.  &  W.3 
On  account  of  the  uncertainty  in  regard  to  the  behavior  of 

tempered  steel  under  variations  of  temperature,  the  observations 

for    the   determination  of  the  coefficient  of  expansion   of  this 

metal  were  continued  for  several  months.     It  will  be  sufficient 

to  give  the  results  of  two  series  of  comparisons. 

By  the  second  method,  described  on  page  18,  the  coefficient 

10.45   mikrons  in   one   meter  for  each   degree  Centigrade  was 

obtained. 

In  the  second  series,  the   end-measure  meter  P.  &  W.3  was 

compared  with  the  Froment  end-meter  designated  Kx. 

Series  I. 

EQUATION  OF  CONDITION.  Ht  —  P.  &  W.3 

1881.                                                 (0°  — T)  atO°C. 

Feb.  14.  +  55.2  p  -  a  -    5.3  6  +  56.7  p 

15.  -|- 57.4      —  a  —    5.66  +58.9 

16.  +43.0      =  a  — 2546  +50.1 
1  7.  +  39.2      r=  a  —  25.2  b  +  46.3 
18.  +  52.7      =  a  —    4.2  b  +  53.9 

20.  +57.4      =a—    0.76  +57.6 

21.  +56.4      —a—    4.86  +57.7 

22.  +53.9      =  a  —  28.16  +61.8 

23.  +  48.1      =  a  -  25.8  6  +  55.3 

24.  +  51.8   .  =  a  —  27.9  6  +  59.6 

25.  +  58.2      =  a  +     1.3  6  +  57.8 
Whence:             6  =  +  0.28  p       a  =  +  55.9  p 


41 


1881. 

March  11. 
13. 
14. 
15. 
16. 
17. 
18. 
18. 
20. 
20. 

Whence 


1881. 

March  21. 
22. 
23. 
24. 
25. 

Whence: 


1881. 

March  28. 
29. 
30. 
31. 

April    1. 
2. 

3. 
4. 
5. 

Whence: 


Series  II. 

EQUATION  OF  CONDITION. 

Rx—  P.  &W.3 

(0°  —  T) 

at  0°  C. 

4-  50.6  p  =  a  —  16.0  b 

4-  56.7  p 

4-  50.0      =  a  —    5.8  b 

4-  52.2 

4-  52.6      =  a  —    7.8  b 

4-  55.6 

4-  49.5      —  a  —     6.2  b 

4-  51.9 

4-48.5      —a  —  23.35 

4-  57.3 

4-  44.5      —a  —  22.6  5 

4-  53.1 

4-46.5      =a  —  21.8  b 

4-  55.1 

4-  45.5      —  a  —  23.5  5 

4-  54.4 

4-  55.9      =  a  —    6.8  b 

4-  58.5 

4-55.9      —a—     7.75 

4-  58.2 

b  =  4-  0.38  ju       a  = 

-1-  55.4  p 

/Sferww  ///. 

EQUATION  OP  CONDITION. 

B!—  P.  &  W.3 

(0°  —  T) 

at  0°  C. 

4-  56.4  p  —  a  —    9.7  b 

4-  60.6  p 

4-  52.8      =  a  —    9.7  b 

4-  57.0 

4-  45.8      —  a  —  28.8  5 

+  58.8 

4-  44.9      =  a  —  24.1  b 

4-  65.8 

4-55.2      =a—    3.75 

4-56.4 

5  =  4-  0.47  p       a  = 

4-  57.7  p 

tfm'es  IF. 

EQUATION  OP  CONDITION. 

RX-P.  &W.3 

(0°  —  T) 

at  0°  C. 

4-  40.5  p  —a  —  24.1  5 

4-  54.4  p 

4-  43.6      =  a  —  27.1  5 

4-  59.3 

4-  40.7      =  a  —  25.7  5 

4-  51.7 

4-  38.7      =  a  —  26.8  5 

4-  54.2 

4-  50.2      =  a  —  17.8  5 

4-  60.0 

4-  49.7      =  a—  17.3  5 

4-  59.7 

4-  52.6      =  a  —    2.9  5 

4-  54.3 

+  56.2      =  a  4-     0.4  5 

4-  56.0 

4-  58.8      =  a  4-    0.9  5 

4-  58.3 

5  —  4-  0.58  p       a  = 

4-  56.9  p 

42 

Collecting  results,  we  have  : 

p.  &  W.3  +  56.4^  =  Rt 
But:  Rt    —    8.4  M  =  A* 

Hence:  P.  &  W.3  -f  48.0  p  =  A 

Or: 

The  end  meter  P.  &  W.3  is  48.0  mikrons  too  short  at  0°  C. 

For  the  coefficient  of  P.  &  W.,  we  have: 

o 

10  11  jj,  -f  0.43  p  =  10.54  n  for  each  degree  Centigrade. 
Expressed  in  fractional  parts  of  any  unit  of  length,  this  value  is 
1054  parts  in  100  millions. 

10.45  +  10.54 
Ihe  value  adopted  is  —      —  ;  —      -  p  =  10.50  p 

From  a  similar  investigation  with  regard  to  the  end-measure 
yard,  I  find  for  62°.0  Fahr.  : 

p.  &  W.3  +  .000227  inch  -  Y 

Or: 

P.  &  W.3  is  227  millionths  of  an  inch  too  short. 

The  final  sets  of  graduations  traced  upon  P.  &  W.3  are  de- 
scribed as  follows: 

(1)  Consists  of  a  set  of  heavy  lines,  designated  P.  &  W.3ai, 
as  shown  in  figure  (2),  page  5. 

(2)  Consists  of  a  similar  set  of  adjacent  fine  lines,  designated 

P.    &   W.2a2. 

(3)  Consists    of    groups    of    equi-distant    lines,    designated 
P.  &  W.3b12345.     The  space  between  the  lines  is  TT/^  of  an  inch. 

Each  set  of  graduations  was  laid  off  independently.  For 
example,  after  having  ruled  the  first  line  in  each  group,  the 
microscope  carriage  was  moved  back  to  its  first  position,  and, 
after  setting  the  micrometer  line  of  the  microscope  rTJVo-  of  an 
inch  in  advance,  the  second  set  of  graduations  was  laid  off. 

The  following  are  the  relations  between  P.  &  W.3a2  and  the 
standards  A  and  Y  : 


P.  &  W.3«2  +    8.2^  =  P.  &  W.2*a 

But                  P.  &W.2a2-—    1.8/z  =  A 

Hence             P.  &  W.3'2  -f    6.4  ^  =  A 

Or, 

The  meter  P.  &  W.3'a  is  6.4  mikrons  too  short 

at  0°  C.    . 

*  Page  289,  Proceedings  American  Academy. 


43 

For  tLe  Yard  we  have : 

P.  &  W.3a2  +  0.000101  in.  =  P.  &  W.a-a 
But  P.  &  W.2a-2  —  0.000029  in.  =  Y 

Hence       P.  &  W.3"2  -f  0.000072  in.  =  Y 

Relations  between  the  Working  Standard  P.  &  W.5  and  ^  Y. 
The  form  of  the  graduations  is  shown  in  Fig.  5. 

FIG.  5. 


I  IN  I  B>  HIM  i 


51 


I II  Ml| 

V  I  I  i    II 


a  to  b  graduated  in  16ths,  8ths,  and  4ths,  the  latter  being  bands  of  3  lines 
each. 

b  to  c  "  inches  only,  bands  of  3  lines  each. 

d  to  e  "  lOths  and  20ths,  each  quarter-inch  being  a  band  of  3 

lines. 

betof  "  to  represent  diameter  at  root  of  thread,  U.  S.  Standard 
Thread  Gauges,  £  inch  to  2  inches  inclusive,  2  lines 
each,  one  line  light  and  one  heavy.  Initial  line  at  b  e, 
reading  towards  a  d. 

I  to  f  "  to  represent  diameter  as  above  for  2£  inches  to  4  inches  in- 

clusive, single  line  each.  Initial  line  at  I,  reading 
ing  towards  a  d. 

g  to  k    Band  of  lines  ^  of  an  inch  long,  ruled  2  inches,  2,500  per  inch. 


Investigation  of  the  Working  Standard  P.  &  W.5 

The  first  set  of  comparisons  between  the  4  inches  of  P.  &  ~W.5 
and  the  first  4  inches  of  P.  &  W.2as  made  with  the  Universal 
Comparator  in  April,  1881,  gave  the  relation  : 

p.  &  W.5  — 0.000012  in.  =J  Y 

In  September,  1881,  a  more  complete  set  was  made  with  the 
new  comparator.  The  following  are  the  results  obtained : 


44 


Second  Series. 


Early  Morning  Observations. 


Mid-  Afternoon  Observations. 


Therm. 

—  P.&W.5 

Therm. 

-P.&W.6 

1881. 

o 

at  62°.  0  Fahr. 

1881. 

o 

at  62°.  0  Fahr 

Sept.  11 

67  0 

—  1.04  div. 

Sept.  11 

67.9 

+  0.55  div. 

12 

67.0 

—  0.80 

13 

81.3 

—  1.75 

13 

81.3 

—  2.15 

13 

79.8 

+  2.24 

13 

79.8 

+  0.13 

15 

64.6 

+  1.33 

15 

66.6 

+  0.11 

18 

61.4 

—  1.99 

15 

64.3 

+  1.67 

19 

62.4 

—  0.68 

15 

64.3 

+  1.63 

20 

63.4 

+  2.63 

18 

57.0 

—  2.74 

21 

63.6 

+  2.76 

19 

62.0 

—  0.20 

22 

61.1 

—  0.75 

20 

63.0 

+  0.94 

20 

63.1 

—  0.93 

Mean  +0.48 

21 

63.6 

+  0.50 

22 

59.4 

+  0.28 

23 

61.8 

+  0.66 

Mean  —0.10 


For  the  mean  value  we  have : 


P.  &  W..     +0.2  div.         -  1  P.  &  W    -a 


But 
Whence, 


&  W.2«2  —  0.1 


P.  &  W. 
P.  &  W. 


+  0.1 

+  0.000002 


=£  Y 
.  =     Y 


Third  Series. 

With  Comparator  No.  1. 

Comparison  of  P.  &  W.6  with  the  first  4  inches  of  P.&W., 


Therm. 

-P.&W.s 

Therm. 

P.  &  W.  B 

1881. 

0° 

At  62°.  0 

1881. 

0° 

At  62°.  0 

Oct.     6 

36.8 

+  4.  9  div. 

Oct.  11 

59.0 

+  1.3  div. 

7 

50.3 

+  2.6 

11 

58.4 

—  1.9 

7 

51.8 

—  1.3 

18 

84.4 

+  2.1 

9 

57.6 

—  6.1 

18 

84.4 

+  1.7 

9 

58.3 

—  1.0 

18 

84.4 

+  3.6 

10 

59.6 

—  0.6 

19 

86.8 

+  0.4 

10 

59.8 

—  2.2 

,  19 

86.8 

.+  2.8 

20 

80.3 

+  2.3 

Whence,         P.  &  W.fi  +  0.6  div.=J  P.  &  W.2 

And 

P.  &  W.6  +  0.000009  in.:=  J  Y 


45 

Fourth  Series. 
With  Comparator  No.  1. 
Comparison  of  P.&W.6  with  the  first  4  inches  of 


Therm. 

^Ri-P.&W.g 

Therm. 

&RI  —  P.&W. 

1881.           0° 

At  62°.0 

1881. 

0° 

At  62°.  0 

Oct.     6      36.8 

+  33.  2  div. 

Oct.   11 

58.4 

+  35.  9  div. 

7      50.3 

+  33.5 

18 

84.4 

+  37.0 

7      51.8 

+  30.5 

18 

84.4 

+  34.7 

9      57.6 

+  30.5 

18 

84.4 

+  33.7 

9      58.3 

+  39.9 

18 

86.8 

+  30.0 

10      59.6 

+  31.4 

19 

86.8 

+  30.3 

10      59.8 

+  35.9 

19 

88.3 

+  26.2 

11      59.0 

+  32.2 

20 

88.3 

+  30.6 

Whence, 

P.  &  W.5  +  32. 

8  div. 

=  iRi 

But 

£  R,          -33. 

8 

=i  Y 

Whence, 

p.  &  W.5-   1. 

0 

=  i  Y 

p.  &  W.5-   0. 

000020  in.=£  Y 

Fifth  Series. 

Comparison  of  P.  &  W.5  with  the  first  four  inches  of  a  steel 
half-yard  designated  \  Y. 

In  March  of  the  present  year  I  requested  that  you  would 
return  to  me  P.  &  W.5  in  order  that  I  might  compare  this  stand- 
ard with  the  sub-divisions  of  a  new  standard  half-yard  whose 
relation  to  J  P.  &  W.2a2  has  been  determined  with  the  greatest 
care  from  observations  extending  over  several  months.  This 
half-yard  has  no  sensible  correction  for  total  length.  The  cor- 
rections for  errors  of  sub-division  are  as  follows :  A  plus  sign 
indicates  that  the  indicated  space  is  too  short;  a  minus  sign  that 
it  is  too  long. 


Space.        Correction. 

1  —0.000006  inch. 

2  +0.000024 

3  +0.000000 

4  +0.000000 

5  —0.000024 

6  +0000005 


Space.        Correction. 

7  +0.000005  inch. 

8  —0.000004 

9  —0.000012 

10  —0.000042 

11  —0.000026 

12  +0.000036 


Space.        Correction. 

13  +0.000000  inch. 

14  +0.000020 

15  —0.000016 

16  +0.000014 

17  +0.000016 

18  +0.000010 


A  comparison  with  the  first  four  inches  of  this  bar  gave  the 
result  : 


P.&  W.6  —  0.000005  in.=£  Y. 


46 

Collecting  results,  we  have : 

From  Series      I.  P.  &  W.5  —  0.000012  in.  =  £  Y 

Series    II.  P.  &  W.5  f  0.000002        —  £  Y 

Series  TIL  P.  &  W.6  +  0.000009        —  J  Y 

Series  IV.  P.  &  W.8  —  0.000020        -  i  Y 

Series     V.  P.  &  W.e  -  0.000005        =£Y 

Whence:  P.  &  W.5  —  0.000005  in.  —  J  Y 

Or: 

P.  &  W.5  is  5  millionths  of  an  inch  too  long  at  62.0°  Fahr. 

Investigation   of  the   Errors   of  the  Line   and   End-Measure   Yard 
and  Meter  P.  &  W.4 

For  the  end-measure  meter,  I  find  for  0°  C.  : 

p.  &  W.4  —  O.G/i  =  A 
Or: 
End-meter  P.  &  W.4  is  0.6  mikrons  too  long  at  0°  C. 

For  the  yard,  I  find  : 

P.  &  W.4  —  0.000112  in.  =  Y  at  62°.0. 
Or: 
Yard  P.  &  W.4  is  112  millionths  of  an  inch  too  long  at  62. °0. 

The  report  upon  the  line  graduations  of  P.  &  W.4  will  be 
delayed  until  the  completion  of  a  series  of  observations  now  in 
progress  for  the  purpose  of  ascertaining  the  effect  of  drift  in 
thermometers  upon  the  summer  and  winter  comparisons  of 
standards  which  have  widely  different  coefficients  of  expansion. 

Corrections  for  Errors  of  Sub -divisions. 
SUB-DIVISIONS  OF  P.  &  W.2*2 


July  17.  July  18. 

div.  div. 

I.     _  1.9  —  1.8 

II.     4.  6.8  +  6.4 

III.     —  4.8  —  5.4 


(i  div.  =  .504  /j) 

, 

FEET. 

Mean  of  all 

previous 

Adopted 

Mean.      Observations. 

Corrections. 

div.                  div. 

div. 

inch. 

—  1.6            -  0.9 

-  1.2    = 

-  0.000024 

+  6.6          +  4.2 

+  5.4   = 

+  0.000108 

-5.1          -3.3 

—  4.2   = 

-f  0.000084 

47 


THREE-INCH  SPACES  OF  THE  FIRST  FOOT. 


July  15. 
div. 

July  15. 
div. 

July  17. 
div. 

July  18. 
div. 

July  19. 
div. 

I. 

-  6.6 

—  5.4 

—  3.2 

-2.8 

—  3.6 

II. 

+  2.9 

+  i.o 

—  1.3 

+  0.3 

—  1.0 

III. 

—  3.0 

-  2.3 

—  1.5 

—  3.6 

-2.1 

IV. 

-f  6.8 

+  8.6 

+  6.0 

+  6.4 

+  6.7 

July  20. 

div. 

July  81. 
div. 

Means, 
div. 

inc 

I. 

-4.3 

—  4.1 

—  4.3 

— 

—  000 

II. 

•f  0.9 

-j-  0.9 

+  0.2 

— 

+  0.00' 

nr. 

-  3.4 

—  2.2 

—  2.6 

— 

—  0.00' 

IV. 

-f  5.7 

+  5.5 

+  6.8 

— 

+  0.00' 

INCHES  OF  THE  FIRST  THREE-INCH  SPACE. 


July  17. 
div. 

July  18. 
div. 

July  19. 
div. 

Mean, 
div. 

I. 

-  0.9 

—  0.5 

+  0.0 

—  0.5 

II. 

+  1.6 

+  0.8 

+  0.8 

+  1.1 

III. 

-  0.7 

-  0.3 

-  0.8 

—  0.6 

inch. 

—  0.000010 
+  0.000022 

—  0.000012 


SIX-INCH  SPACES  OF 
THE  FIRST  FOOT. 

Inch. 

I.      -  0.000089 
II.      _  0.000084 


1. 

IT. 
III. 
IV. 

V. 


FOUR-INCH  SPACES  OF 
THE  FIRST  FOOT. 

Inch. 

I.      —  0.000003 

II.      —0.000112 

III.      +0.000115 


INCH  SPACES  OF  THE 
FIRST  Six  INCHES. 

Inch. 

I.  _  0.000028 

II.  -  0.000064 

III.  +  0.000008 

IV.  —  0.000020 
V.  —  0.000028 

VI.  +  0.000004 


SUBDIVISIONS  OF  P.&W., 

3 

Decimeters  of  P.&W.3a2 

Counted  from  the  center  towards  the  end. 

CORRECTIONS. 

Series  I.  Series  II. 

+  1.7/1  +1.2/« 


—  1.3 

—  0.6 
+  0.2 

—  0.8 


—  0.7 
+  0.8 
+  0.2 

—  0.7 


Mean. 
+  1.4 

—  1.0 
+  0.1 
+  0.2 

—  0.7 


48 


6  inch  spaces  of  P.&Wg.a2 

Corrections. 

I.          +  0.000002  inch. 
II.  -0.000076 

j  III.         +  0.000074 


6-inch  spaces  of  P.&\V3.bi2f±* 

Corrections. 

I.          +  0.000010  inch. 
II.         —0.000031 
III.          +  0.000021 


First  six -inch  spaces  of  P.  &W.  3a2  Fii  st  six-inch  spaces  of  P.&W.3b-Ugi* 

I.  +  0.000026  inch.  I.  -f  0.000020  inch. 

II.  -0.000040  II.  +0.000002 

III.  -0.000016  III.  -0.000048 

IV.  -0.000028  IV.  -0.000010 
V.  -f  0.000064  V.  +  0.000016 

VI.  —0.000006  VI.  +0.000020 


SUBDIVISIONS  OF  P.&W. 


I. 

II. 

111. 

IV. 


Inch  spaces. 

Corrections. 

—  0.000009  inch. 
+  0.000037 

—  0.000025 

—  0.000003 


I. 

II. 

III. 

IV. 

V. 

VI. 

VII. 

VIII. 


J-inch  spaces. 

Corrections. 

—  0.000002  inch. 
+  0.000004 

+  0.000006 

—  0.000005 
+  0.000005 
+  0.000004 

—  0.000012 
+  0.000004 


It  is  to  be  noted  that  all  the  corrections  given  above  are  relative 
corrections,  since  no  account  has  been  taken  of  the  absolute  errors 
of  the  entire  space  sub-divided.  These  values  are  therefore  to  be 
corrected  by  the  proportional  part  of  the  errors  for  total  length. 

It  is  my  intention  to  present,  at  some  future  time,  a  supple- 
mentary report  upon  the  standards  P.&W.2  and  P.&W.4  when 
the  observations  now  in  progress  are  completed. 

In  conclusion,  allow  me  to  express  my  appreciation  of  your 
kindness  in  offering  the  facilities  which  you  have,  with  great 
liberality,  placed  at  my  disposal  for  this  investigation. 
I  remain,  gentlemen, 

Your  obedient  servant, 

WM.  A.  ROGERS. 

CAMBRIDGE,  MASS.,  July  7,  1886. 


49 


THE  OBSERVATORY  OF  YALE  COLLEGE. 


THERMOMETRIC    BUREAU. 


Examination  of  the  Mercurial  Thermometer,  No.  — , 
Made  by 

(Used  by  The  Pratt  &  Whitney  Co.  for  determination  of  reduction  to  Standard  temperature.) 


THERMOMETER  READING. 

CORRECTION. 

o 

32°  F. 

+  0C.4F. 

52° 
62 

+  0.2 

+  0.1 

72° 
82 

+  0.1 

0.0 

92° 

—  0.1 

Graduated  from 


—  5°  to  +  280°  C. 
25°  to  +  235°  F. 


1°.  This  thermometer  has  been  examined  in  a  vertical  position  with  the 
metallic  scale  and  tube  immersed  in  water  having  the  temperature  of  the  bulb. 

2°.  When  the  correction  is  +  it  must  be  added  to  the  thermometer  read- 
ing, and  when  —  it  must  be  subtracted.  For  example,  suppose  the  thermome- 
ter to  register  81°.  0  and  the  respective  tabular  corrections  at  72°  and  92°  to 
be  — 0°.5  and  — 0°.7,  then  the  corrected  reading  of  the  thermometer  would  be 
81°.0  —  0°.6  =  80°.4. 


The  theoretical  mercurial  standard  thermometer  to  which  this  instrument 
has  been  referred,  is  graduated  by  equal  volumes  upon  a  glass  stem  of  the 
same  dimensions  and  chemical  constitution  as  the  Kew  standards  578  and  584. 
The  permanent  freezing  point  is  determined  by  an  exposure  of  not  less  than 
48  hours  to  melting  ice,  supposing  the  temperature  of  the  standard  has  not 
been  greater  than  25°  C.  =77°  F.  during  the  preceding  six  months.  The 
boiling  point  is  determined  from  the  temperature  of  the  steam  of  pure  water 
at  a  barometric  pressure  of  760  mm.  =  29.922  in.  (reduced  to  0°  C.)  at  the  level 
of  the  sea  and  in  the  latitude  of  45°.  This  standard  coincides  with  the  perfect 
gas  thermometer  within  0°.l  F.  for  temperatures  between  zero  and  212°  F. 

LEONARD  WALDO, 

Astronomer  in  Charge. 
NEW  HAVEN,  CONN.,  June  10,  1882. 
4 


50 


AMERICAN  SOCIETY  OF  MECHANICAL  ENGINEERS. 

SECRETARY'S  OFFICE,  No.  239  Broadway, 

NEW  YORK,  Dec.  15,  1882. 
THE  PRATT  &  WHITNEY  Co.,  Hartford,  Conn. 

Gentlemen, — By  action  of  this  Society,  I  am  directed  to  transmit  to  you  a 
certified  copy  of  the  Report  of  the  Committee  on  Standards  and  Gauges. 
I  have  the  pleasure  of  forwarding  it  herewith. 

Respectfully  yours, 

THOS.  W.  RAE,  Secretary. 


EEPOET  OF  COMMITTEE  ON  STANDARDS  AND  GAUGES, 

PRESENTED    AT    THE    ANNUAL    MEETING    OF    THE    AMERICAN    SOCIETY 

OF    MECHANICAL    ENGINEERS,    HELD    IN    NEW    YORK, 

NOVEMBER,    1882. 


Your  Committee  on  Standards  and  Gauges  have  to  report  that 
they  have  examined  the  Rogers-Bond  Comparator  in  use  by  The 
Pratt  &  Whitney  Company  at  Hartford,  Conn.,  together  with 
gauges  for  end-measure  produced  by  this  machine. 

This  apparatus  is  used,  first,  to  compare  line-measures  of  length 
with  attested  copies  of  the  standard  bars  of  England  and  the 
United  States;  second,  to  sub-divide  these  line-measures  into 
their  aliquot  parts,  and  to  investigate  and  determine  the  errors, 
if  any,  of  these  subdivisions;  and  third,  to  reduce  these  line- 
measures  to  end-measures  for  practical  use  in  the  shops. 

A  paper  read  by  Professor  W.  A.  Rogers,  before  the  American 
Academy  of  Arts  and  Sciences,  April  14,  1880,  on  "  The  Present 
State  of  the  Question  of  Standards  of  Length,"  and  a  paper 
read  by  Mr.  George  M.  Bond  before  this  society  at  its  regular 
meeting  in  Hartford,  in  1881,*  will  give  all  needed  information 
on  the  subject  of  standards  of  line-measure. 

The  comparator  is  provided  with  two  microscopes,  their  mag- 
nifying power  being  about  150  diameters,  each  having  a  micro- 
meter eye-piece,  the  divisions  of  which  represent  about  Fu.iinr 

•Trans.  Am.  Soc.  Mech.  Eng.,  Vol.  II,  p.  80. 


51 

of  an  inch,  and  in  reading,  these  divisions  are  usually  subdivided 
by  the  eye  into  tenths.  In  every  case  at  least  three  readings  are 
taken,  and  the  mean  of  the  three  is  used  in  calculating  the  result, 

The  microscopes  are  mounted  upon  a  carriage  which  slides 
freely  upon  two  cylindrical  guides,  which  are  heavy  tubes  of 
hard  tool  steel,  carefully  ground  true  and  cylindrical.  These 
are  supported  at  their  ends  in  bearings  formed  in  the  heavy  cast- 
iron  base  of  the  machine.  Counter-weight  levers  are  applied 
under  these  tubes  at  about  one-quarter  the  total  length  from  each 
end,  to  overcome  the  flexure  arising  from  their  own  weight  and 
that  of  the  carriage  and  stops.  These  stops  are  arranged  so  as 
to  be  clamped  firmly  to  the  guides  at  any  desired  distance  apart, 
and  serve  to  limit  the  motion  of  the  microscope  plate  or  carriage 
when  brought  in  contact  with  either  stop.  The  carriage  is 
moved  up  against  the  stops  by  a  rack  and  pinion  which  is  pro- 
vided for  the  purpose,  the  rack  being  secured  to  the  bed  of  the 
comparator  between  and  independent  of  the  guide  bars.  The 
abutting  surfaces  of  the  carriage  and  stops  are  hardened  steel, 
those  on  the  carriage  being  spherical,  while  those  on  the  stops  are 
flat,  and  each  stop  is  provided  with  an  electro-magnet  which  serves 
to  hold  the  carriage  firmly  against  the  stop,  so  as  to  prevent  its 
settling  back  during  an  observation. 

On  one  side  of  the  comparator  is  a  table  provided  with  rapid 
vertical  and  lateral  adjustments  and  with  a  traverse  parallel  with 
the  motion  of  the  microscope  plate  of  about  forty-five  inches  ;  on 
top  of  this  table  is  an  adjustable  plate  on  which  the  standard 
bars  are  laid  to  be  compared.  This  plate  is  provided  writh  fine 
adjustments  for  parallelism,  focus  and  position,  and  several  line- 
measure  standards  may  thus  be  compared  at  once  under  the 
microscope  without  handling  the  bars.  This  is  an  important 
feature,  as  it  will  be  evident  that  errors  due  to  variations  of  tem- 
perature resulting  from  handling  or  from  any  other  cause,  must 
be  carefully  guarded  against.  On  the  opposite  side  of  the  com- 
parator is  a  fixed  table  or  projecting  ledge  forming  part  of  the 
base  on  which  this  adjustable  plate  may  be  placed,  so  that  stand- 
ard bars  may  be  investigated  on  either  side  of  the  machine.  For 
regular  work,  this  place  is  occupied  by  the  caliper  for.  reducing 
from  line  to  end-measure.  The  microscopes  are  mounted  upon 
the  carriage  in  such  a  manner  that  they  may  ba  used  both  on  one 


52 

side,  or  one  on  each  side  of  the  carriage,  at  variable  distances 
apart,  according  to  the  character  of  the  work  to  be  examined. 

The  comparator  is  firmly  supported  on  solid  brick  piers,  capped 
with  stone,  and  the  movable  table  having  a  traverse  of  about 
forty-five  inches,  referred  to  above,  is  on  an  entirely  separate 
foundation,  to  avoid  all  disturbance  of  the  microscopes  'that 
might  arise  from  moving  the  table.* 

Subdivisions  of  a  standard  bar  may  be  compared  by  placing 
the  microscopes  say  twelve  inches  apart,  if  the  subdivisions 
under  investigation  are  one-third  of  the  yard,  the  variation  being 
measured  or  read  by  means  of  the  micrometer  eye-piece ;  the 
standard  is  then  moved  under  the  fixed  microscope,  so  as  to 
compare  each  separate  twelve  inches  successively,  their  relation 
being  thus  determined. 

.Another  method  is  to  fix  the  stops  so  that  the  microscope 
carriage  will  have  a  movement  of  as  near  the  length  of  the  sub- 
divisions to  be  examined  as  may  be  convenient.  In  this  case 
only  one  microscope  is  used,  the  carriage  moving  a  fixed  distance 
between  the  two  stops  and  the  subdivisions  of  the  standard ;  being 
thus  compared  with  a  constant  quantity,  their  relation  is  con- 
sequently determined. 

Line-measure  standards  may  be  compared  on  this  machine  : 

(a)  By  referring  the  standards  to  a  fixed  distance  between  two 
stops. 

(b)  By  bringing  the  defining  lines  under  two  fixed  microscopes 
placed  a  distance  apart  nearly  equal  to  the  length  of  the  stand- 
ards to  be  compared. 

(c)  By  placing  two  standards  to  be  compared  side  by  side,  arid 
placing  one  microscope  over  each  bar,  the  carriage  being  then 
moved  the  length  of  the  bars,  the  relative  length  of  the  standards 
is  readily  determined. 

(a)  By  placing  one  standard  on  one  side  of  the  line  of  motion 
of  the  microscope  carriage  and  one  on  the  opposite  side,  using 
one  microscope  for  each  bar ;  by  reversing  the  position  of  the 
bars  the  mean  difference  may  be  found. 

(e)  By  comparing  standards  by  the  use  of  two  microscopes 
placed  horizontally  and  at  a  fixed  distance  apart,  so  that  stand- 

*  For  general  view  of  the  Comparator  see  Frontispiece. 


53 

ards  may  be  compared  in  the  same  position  and  under  the  same 
conditions  that  comparisons  are  made  at  the  United  States  Coast 
Survey  Department  at  Washington.* 

The  microscope  carriage  should  move  in  an  absolutely  straight 
line,  and  the  cylindrical  guides  give  perhaps  the  closest  approxi- 
mation to  this  condition.  Errors,  however,  will  exist,  and  the 
correction  for  possible  horizontal  curvature  of  the  guide-bars  is 
found  by  comparing  a  standard  with  a  fixed  distance  between  the 
stops,  first  on  the  left  hand  side  of  microscope  carriage,  and 
afterwards  on  the  right-hand  side,  under  the  same  conditions  in 
both  cases,  of  temperature,  points  of  support  of  the  standard, 
and  of  focus.  The  face  of  the  bar  must  in  both  cases  be  main- 
tained in  the  same  horizontal  plane,  to  avoid  errors  due  to  verti- 
cal flexure  of  the  guides  ;  the  difference  of  the  two  comparisons 
with  the  fixed  or  constant  distance  furnishing  data  for  calculating 
the  radius  of  curvature  and  the  position  of  the  center  —  that  is, 
on  which  side  it  is  located  —  and  hence  determining  the  sign  ot 
the  proper  correction,  whether  it  be  plus  or  minus,  should  the 
amount  be  appreciable. 

The  vertical  curvature,  or  flexure,  may  be  determined  in  the 
same  way,  using  the  standard  bar  placed  at  varying  heights  and 
comparing  it  with  the  constant  distance  moved  by  the  microscope 
carriage,  the  microscope  and  bar  being  kept  always  in  the  same 
vertical  plane,  to  eliminate  errors  of  horizontal  curvature. 

In  transferring  from  line  to  end-measure,  as  the  two  micro- 
scopes do  not  move  in  the  same  vertical  plane,  correction  for 
horizontal  curvature,  if  of  an  appreciable  amount,  must  be 
applied  with  the  proper  sign,  as  remarked  above,  as  in  such  case 
one  microscope  evidently  would  move  a  distance  differing  from 
that  of  the  other  by  the  difference  of  the  lengths  of  the  sub- 
tended chords. 

Errors  due  to  vertical  curvature  or  deflection  of  the  guide-bars 
may  be  practically  eliminated  by  taking  care  to  keep  the  sur- 
faces, on  which  the  lines  to  be  observed  by  the  microscope  are 
ruled,  in  precisely  the  same  horizontal  plane. 

The  caliper  attachment  to  the  comparator  provides  means  for 
reducing  line-measure  to  the  practical  form  of  end-measure,  and 
consists  of  a  fixed  stop  and  a  movable  plunger,  cylindrical  in 

*  See  page  8,  Prof.  Rogers1  Report. 


54 

form,  sliding  in  well  fitted  bearings,  and  having  a  traverse  of 
about  six  inches.  The  abutting  faces  of  the  plunger  and  fixed 
stop  are  of  hardened  steel,  three-eighths  of  an  inch  in  diameter, 
and  are  ground  to  true  plane  surfaces  which  are  perpendicular  to 
the  line  of  motion  of  the  plunger. 

The  plunger  is  pressed  against  the  fixed  stop  and  also  against 
anything  hfld  between  the  surfaces  of  the  plunger  and  the  fixed 
stop,  by  a  rod  which  compresses  a  spiral  spring  within  the 
plunger.  This  rod  is  clamped  to  place  so  as  to  hold  the  pressure 
of  the  spring  constant  while  an  observation  is  being  made,  the 
amount  of  compression  of  the  spring  being  made  approximately 
equal  in  each  case.  This  simple  contrivance  dispenses  with  the 
need  of  the  gravity  piece  used  by  Whitworth. 

No  great  care  need  be  taken  as  to  the  amount  of  the  compres- 
sion of  the  spring,  as  no  perceptible  difference  is  shown  under 
the  microscope  when  the  spring  is  compressed  an  amount  varying 
from  a  quarter  of  an  inch  to  two  and  one-half  inches.  The  line 
upon  the  plate  on  the  plunger  being  about  FTSYOQ-O  °f  an  mcn  in 
width,  and  the  line  of  the  micrometer  eye-piece  being  in  exact 
coincidence  with  the  ruled  line  upon  the  plate,  no  change  of 
relative  position  was  perceptible  during  a  continued  observa- 
tion using  a  microscope  magnifying  about  150  diameters,  while 
the  spring  was  subjected  to  varying  compression  within  the 
above  limits. 

The  error  due  to  flexure  of  the  end-measures  is  not  appreciable 
in  pieces  up  to  six  inches  in  length,  but  standard  bars  of  twelve 
inches  and  longer  require  supports,  and  great  care  must  then  be 
taken  to  have  the  bar  to  be  measured,  parallel  to  the  line  of 
motion  of  the  plunger  and  the  microscope  carriage. 

This  caliper  is  used  with  two  microscopes,  one  of  which  is  over 
a  finely  ruled  standard  bar,  and  the  other  over  a  finely  ruled 
plate  which  is  attached  to  the  plunger,  care  being  taken  to  have 
this  plate,  throughout  its  entire  line  of  motion,  in  the  same 
horizontal  plane  as  is  the  surface  of  the  standard  ruled  bar.  The 
faces  of  the  caliper  are  brought  in  contact  by  the  rod  and  spiral 
spring,  and  the  microscope  adjusted  until  it  bisects  the  line  upon 
the  plate  attached  to  the  plunger.  The  other  microscope  is  set  so 
as  to  bisect  the  initial  line  on  the  standard  ruled  bar,  both 
microscopes  being  firmly  attached  to  the  carriage ;  the  plunger 


55 

is  now  drawn  back,  the  piece  to  be  tested  put  between  the  faces 
of  the  caliper,  and  the  plunger  forced  up  until  the  spiral  spring 
is  compressed  about  the  same  amount  as  before.  The  carriage  is 
now  moved  until  the  line  on  the  plate  is  again  bisected  by  its 
microscope,  and  the  microscope  over  the  standard  bar  by  the  aid 
of  the  micrometer  determines  the  exact  length  of  the  piece  in 
terms  of  the  subdivisions  of  the  ruled  standard.  This,  operation 
can  be  performed  very  rapidly  and  with  uniform  results.  One 
accustomed  to  the  use  of  the  micrometer  will  readily  measure 
within  one  division.  A  test  to  determine  the  accuracy  of  setting 
to  a  single  line  on  the  ruled  bar,  made  by  six  members  of  this 
Committee  —  most  of  whom  were  quite  inexperienced  in  the  use 
of  the  microscope  —  showed  between  the  highest  and  lowest  of 
eighteen  readings,  a  difference  of  5.5  divisions,  a  quantity  less 
than  Tovroo-  °^  an  ^ncn>  while  the  average  of  the  eighteen  read- 
ings differed  from  the  average  readings  of  Mr.  Bond  by  four- 
tenths  of  one  division,  or  about  T^OYOO-TT  of  an  inch. 

The  end-measure  pieces  which  your  Committee  were  shown  at 
the  works  of  The  Pratt  &  Whitney  Company,  were  stated  to  be 
correct  within  5-57000-  of  an  inch,  and  perhaps  the  severest 
practical  test  was  made  by  laying  a  number  of  these  pieces  in  a 
groove  planed  in  a  massive  block  of  cast-iron,  one  piece  being 
clamped  down  to  form  an  end  stop,  and  when  the  pieces  laid 
down  reached  the  length  of  twelve  inches,  another  piece  was 
clamped  down.  A  quarter-inch  end-measure  was  used  as  a  try 
piece,  and  was  held  by  a  strip  of  wood  inserted  in  a  small  hole 
passing  through  the  piece ;  the  end  stops  were  adjusted  until  this 
try  piece  would  just  move  easily, —  almost  by  its  own  weight. 
These  pieces  were  then  removed,  and  others  which  had  been  laid 
on  the  cast-iron  block  so  they  might  all  have  the  same  tempera- 
ture, were  substituted,  care  being  taken  not  to  disturb  the  end 
stops";  some  twelve  different  sets  were  tried  in  this  way,  the 
same  quarter-inch  piece  being  used  as  a  gauge,  and  these  twelve 
sets  were  practically  uniform  in  length,  with  one  exception.  In 
this  case  the  quarter-inch  piece  was  quite  loose,  and  accordingly 
the  end-measure  pieces  composing  this  set  were  all  carefully 
measured  on  the  comparator,  as  well  as  a  set  that  had  stood  the 
test.  The  difference  in  length  between  the  two  sets,  one  com- 
posed of  nine  pieces  and  the  other  of  seven,  was  found  to  be  less 


56 

than  TTr,&<nr  of  an  inch,  and  one  piece,  of  the  set  composed  of 
seven,  was  found  to  be  377,^0-  of  an  inch  short,  being  exactly 
one-half  the  total  error  of  the  entire  seven,  as  compared  with  the 
standard  bar,  and  this  was  found  to  be  one  that  had  been  pre- 
viously condemned  on  account  of  a  defect  in  the  end  surface. 

Dividing  the  total  difference  by  the  number  of  pieces  in  the 
set,  the  difference  noted  above  of  TOYOOIF  of  an  inch  between 
the  total  errors  of  the  two  sets  referred  to,  shows  an  average 
difference  for  each  piece  of  the  first  set,  as  compared  with  the 
length  of  the  second  set,  of  about  yy.-ro TF  of  an  inch,  and  about 
Tirs.VoiF  of  an  inch  as  compared  with  the  subdivisions  upon  the 
standard  bar,  to  which  they  were  all  referred. 

The  end-measure  pieces  being  referred  to  lines  ruled  upon 
a  hardened  steel  bar,  and  in  a  manner  which  reduces  possible 
error  to  a  minimum,  the  liability  of  a  deterioration  of  the  standard 
is  eliminated  ;  for  error  would  certainly  result  jvere  they  all  com- 
pared with  a  standard  end-measure  test  piece,  the  use  of  which, 
however  slight,  would  be  attended  with  more  or  less  wear,  and 
the  original  size  thus  lost.  This  ruled  bar  being  preserved,  the 
originals  may  be  duplicated  at  any  time.  As  the  standard  ruled 
bar  is  not  handled  or  touched  in  any  way  during  the  process  of 
measuring,  the  only  risk  of  change  would  seem  to  be  that  due  to 
internal  strains  in  the  standard  itself. 

This  point  will  require  close  investigation  and  comparison  with 
other  standards,  to  determine  the  stability  of  the  hardened  bar. 
This  standard  has  been  submitted  to  a  process  of  annealing,  at  a 
temperature  above  any  ordinary  atmospheric  heat  due  to  climate, 
and  this  annealing  is  believed  to  eliminate  the  risk  of  after 
changes.  A  recent  examination  of  this  standard  which  was  so 
treated  two  years  ago,  shows  no  appreciable  change.* 

Two  adjoining  sides  of  the  end-measure  pieces  are  first  ground 
by  special  machinery  to  plane  surfaces  which  are  perpendicular 
to  each  other,  and  the  end  surfaces  are  afterwards  ground  to  true 
planes  parallel  with  each  other  and  at  right  angles  with  these 
side  planes,  by  the  use  of  a  fixture  which  consists  of  a  block 
having  a  slot  through  its  center,  the  sides  of  which  are  exactly 
perpendicular  to  the  base  of  the  block.  The  block  slides  over  a 
plane  surface,  in  the  center  of  which  is  a  copper  plug  charged 

*  For  later  investigation,  see  page  45,  Prof.  Rogers'  Report,  under  Fifth  Series. 


57 

with  emery  or  diamond  dust.  The  end-measure  piece  is  secured 
in  this  slot,  and  passed  over  the  copper  lap  until  the  end  is 
reduced  to  a  polished  plane  surface  ;  the  piece  is  then  reversed 
and  the  other  end  ground  in  like  manner,  careful  measurements 
being  made  from  time  to  time,  as  the  piece  is  gradually  reduced 
in  length,  great  care  being  taken  to  have  the  temperature  corre- 
spond to  that  of  the  ruled  bar. 

The  test  of  these  end-measures  in  the  groove  of  the  block  of 
cast  iron  referred  to  (page  55),  shows  the  accuracy  of  this  method 
of  manufacture,  as  any  error  of  parallelism  in  any  of  the  ends 
would  seriously  affect  the  total  length  of  the  set. 

Between,  and  below  the  jaws  of  the  caliper  is  a  small  table 
which  can  be  adjusted  vertically  for  the  purpose  of  calipering 
cylinders ;  this  table  is  adjusted  so  as  to  bring  the  center  of  the 
cylinder  to  be  measured  to  about  the  same  height  as  that  of  the 
plunger,  the  axis  of  the  cylinder  being  horizontal;  the  plunger  is 
then  pushed  against  the  cylinder  by  means  of  the  rod  and  spiral 
spring  before  described.  The  pressure  of  this  spring  is  sufficient 
to  move  the  cylinder  on  the  table  until  its  sides  are  tangent  to 
the  plane  end  surfaces  of  the  plunger  and  the  fixed  stop.  By 
moving  the  cylinder  back  and  forth  it  can  be  tested  for  paral- 
lelism, and  by  turning  it,  the  plunger  being  in  each  case  released 
and  brought  into  contact  again,  it  can  be  tested  for  rotundity,  the 
whole  operation  requiring  but  a  few  moments. 

The  personal  error  in  the  use  of  a  microscope,  that  is,  the  vari- 
ations different  individuals  would  make  in  reading  the  intersec- 
tions of  the  lines  by  the  micrometer,  is  eliminated  by  this  process 
of  measuring,  the  microscope  being  in  each  case  set  to  the  zero 
on  the  ruled  bar  when  the  caliper  faces  are  in  contact,  and  also 
to  the  proper  line  when  the  object  to  be  measured  is  between  the 
jaws  of  the  caliper ;  hence  any  individual  difference  there  may 
be  in  setting  will  be  the  same  for  the  readings  at  each  limit, 
i.  e.,  at  zero  and  at  the  position  due  to  the  length  of  the  measured 
piece;  hence  the  difference  between  two  readings  gives  the 
length  of  the  piece  in  terms  of  the  standard  bar.  As  the  stand- 
ard bar  used  by  The  Pratt  &  Whitney  Company,  for  all  measure- 
ments of  four  inches  and  under,  is  of  the  same  material  as  the 
end- measure  pieces  and  cylindrical  gauges,  no  correction  for  tem- 
perature is  required,  the  only  precaution  being  that  the  piece  to 


58 

be  measured  shall  be  maintained  at  the  same  temperature  as  the 
standard  bar,  which  is  readily  accomplished  by  keeping  them 
together  for  a  few  hours  before  measuring. 


CONCLUSION. 


The  completion  of  the  Rogers-Bond  Comparator  marks  a  long 
stride  in  advance  over  any  method  hitherto  in  use  for  comparison 
and  subdivision  of  line-measure  standards,  combining  as  it  does 
all  the  approved  methods  of  former  observers  with  others  origi- 
nal with  the  designers.  Comparisons  can  thus  be  checked  thor- 
oughly by  different  systems,  so  that  the  final  results  of  the  series 
may  be  relied  on  as  being  much  nearer  absolute  accuracy  than 
any  hitherto  produced. 

The  calipering  attachment  to  the  comparator  deserves  special 
commendation,  being  simple  in  the  extreme,  and  solving  com- 
pletely the  problem  of  end  measurements  within  the  limit  of 
accuracy  attainable  in  line  reading  by  means  of  the  microscope 
with  the  micrometer  eye-piece.  The  standard  to  which  the  end 
measurements  are  referred  is  not  touched,  and  each  measurement 
is  referred  back  to  the  same  zero,  so  that  error  from  end  wear 
does  not  enter  into  the  problem.  This  attachment  is  in  advance 
of  all  hitherto  known  methods  of  comparing  end-measures,  either 
with  other  end-measures  or  with  line  standards,  both  as  to  rapid- 
ity of  manipulation  and  the  accuracy  of  its  reading.  The  strong 
point  in  its  construction  being  that  it  refers  all  end-measures  to  a 
carefully  divided  and  investigated  standard  bar  which  is  not  touched 
during  its  use,  and  cannot  be  in  the  slightest  degree  injured  by 
this  service,  thus  giving  convincing  assurance  that  the  measures 
and  gauges  produced  by  its  use  will  be  accurate  and  interchangable. 

In  the  opinion  of  this  committee,  the  degree  of  accuracy 
already  attained  is  such  that  no  future  improvements  can  occa- 
sion changes  sufficiently  great  to  affect  the  practical  usefulness 
of  the  magnitudes  here  determined,  or  the  interchangeability 
of  structures  based  upon  them  with  those  involving  further 
refinements. 

Professor  W.  A.  Rogers  and  Mr.  George  M.  Bond  are  unques- 
tionably entitled  to  great  credit  for  the  admirable  manner  in 
which  they  have  solved  the  problems  of  exact  and  uniform  meas- 
urement, while  the  enterprise  of  The  Pratt  &  Whitney  Com- 


59 

panj  in  bringing  the  whole  matter  into  practical  shape,  is  deser 
ing  of  the  thanks  of  the  engineering  community. 

J.  SELLERS  BANCROFT, 

Secretary  of  the  Committee. 

HENRY  MORTON,  President. 

S.  W.  ROBINSON. 

OBERLIN  SMITH. 

E.  H.  PARKS. 

AMBROSE  SWASEY. 

CHAS.  T.  PORTER. 

ALFRED  BETTS. 

GEO.  R.  STETSON. 


REPORT 

OP 

THE    COMMITTEE    OF    THE    MASTER    CAR-BUILDERS' 

ASSOCIATION 

ON 

STANDARD    SCREW    THREADS. 

PRESENTED  AT  THE  ANNUAL  CONVENTION  HELD  IN  PHILA- 
DELPHIA,  JUNE,   1882. 


[Report  of  the  Committee  of  the  Master  Car-Builders'  Association  appointed 
"  to  investigate  and  report  on  the  present  construction  of  screws  and  nuts  used 
in  cars ;  and  the  amount  of  accuracy  that  is  desirable  to  secure  and  the  best 
means  of  maintaining  it  in  the  standard  adopted  by  the  Association  in  Rich- 
mond, Va.,  June  15,  1871,  and  to  draw  up  communications  addressed  to  the 
managers  and  superintendents  of  railroads,  showing  the  necessity  for  the  use 
of  even  sizes  of  screw  threads,  and  the  amount  of  saving,  as  near  as  it  can  be 
estimated,  which  will  result  to  the  roads  by  strictly  adhering  to  this  practice," 
made  at  the  annual  Convention  in  June,  1882.] 

The  committee  to  whom  this  subject  has  been  referred,  and 
who  have  had  it  under  consideration  for  several  years,  find  that 
to  give  a  clear  understanding  of  it,  a  brief  historical  review  of 
what  has  been  done  is  requisite.  Without  other  introduction, 
then,  it  may  be  said  that  in  1864  the  inconvenience  and  confu- 
sion resulting  from  the  diversity  in  the  screw  threads  used  in 


60 

machine  and  other  construction  was  brought  up  for  consideration 
before  the  Franklin  Institute  of  Philadelphia.  A  committee  was 
then  appointed  to  investigate  and  report  on  the  subject.*  That 
committee  recommended  the  system  designed  by  Mr.  Wil- 
liam Sellers,  and  the  institute  afterwards  adopted  their  recom- 
mendation. Practically  the  three  systems  from  which  they  were 
obliged  to  choose  were,  first,  the  ordinary  sharp  V  thread  shown  in 
Figs.  1  and  2.  Fig.  1  represents  a  section  of  an  inch  bolt  full  size, 


and  Fig.  2  a  section  of  the  thread  enlarged  eight  times  its  actual 
size.  Figs.  3  and  4  show  Whit  worth's  thread  and  Figs.  5  and  0 
Sellers'  system.  The  angle  A  and  A'  between  the  sides  of  the 
V  thread  is  generally  60°,  although  this  is  not  uniformly  so, 
when  it  is,  the  depth  D  from  the  root  of  the  threads  to  the  point 
is  slightly  less  than  J  of  the  pitch.  In  the  Whitworth  thread  the 
depth  D  is  f  of  the  pitch,  and  the  top  and  bottom  of  the  threads 

*  See  reprint  of  Committee  Report,  page  78,  el  seq. 


61 

are  then  rounded  as  shown.     The  angles,  A  and  A',  of  the  sides 
of  the  threads  to  each  other  are  55°. 

The  objections  to  the  V  thread  are  that  the  point  or  outer 
edge  of  the  thread  is  sharp  and  therefore  very  frail  and  liable  to 
injury  from  contact  with  other  objects.  The  space  S  or  groove 
between  the  threads,  at  the  root,  is  also  sharp,  which  facilitates 
fracture  under  strain  and  is  a  source  of  weakness  in  the  screw. 
The  depth  D  of  the  V  thread,  being  slightly  greater  than  that  of 
the  Whitworth  thread,  the  effective  diameter  N  of  the  screw,  at 
the  root  of  the  thread,  is  materially  less  in  the  former  than  in  the 
latter. 

In  Figs.  4  and  6  the  contour  of  a  thread  is  shown  by  the  clotted 
line  cb  and  db.  It  will  be  seen  that  if  a  V  thread  is  used  instead 
of  the  Whitworth  or  Sellers,  the  former  would  cut  into  the  bolt 
farther,  by  a  distance  represented  by  ab,  than  the  others  do. 

The  objections  to  the  Whitworth  thread  are  that  the  angle  of 
55°  can  not  be  measured  or  laid  oft'  with  ordinary  tools,  and  that 
the  rounded  corners  at  the  point  and  root  of  the  threads  are  ex- 
tremely  difficult  to  produce  with  any  degree  of  precision  in  the 
tools  required  to  make  screws.  These  considerations  led  Mr. 
Sellers  to  design  the  system  of  threads  the  form  of  which  is  shown 
by  Figs.  5  and  6.  In  this  the  angle  of  the  V  thread,  60°,  is  re- 
tained, but  instead  of  rounding  the  point  and  root,  these  are  made 
flat,  one-eighth  of  the  depth  of  the  thread  being  taken  oif  at  the 
top,  and  one-eighth  at  the  bottom,  which  leaves  the  depth  of  the 
thread  somewhat  less  than  |-  of  the  pitch.  This  leaves  the  effec- 
tive diameter  N  of  the  bolts  somewhat  greater  even  than  that  of 
the  Whitworth  thread.  The  flat  top  and  bottom  in  screw-making 
tools  can  be  easily  and  accurately  made,  and  the  angle  of  the 
thread  can  be  produced  by  simply  laying  off  a  triangle  having 
equal  sides,  or  subdividing  the  circumference  of  a  circle  with  its 
own  radius,  and  drawing  lines  from  adjacent  points  of  subdivision 
to  the  center.  The  difference  in  the  effective  diameter  of  the 
Whitworth  and  Sellers'  systems  of  course  gives  them  greater 
strength  to  resist  tension  and -torsion  than  screws  with  V  threads 
of  60°  have.  It  is  true  that  the  V  thread  might  be  made  with 
sides  having  a  more  obtuse  angle  to  each  other,  but  in  that  case 
the  nuts  would  be  subjected  to  greater  strain. 


62 


In  a  report  made  in  1868  to  the  Chief  of  the  Bureau  of  Steam 
Engineering  of  the  United  States  Navy,  by  a  board  of  engineers, 
the  difference  in  the  resistance  to  tension  and  torsion  of  bolts 
with  Sellers'  threads,  compared  with  those  having  V  threads, 
was  calculated,  and  is  given  in  the  following  table : 

Talk  showing  the  increased  percentage  of  tensional  and  torsional  strength 
of  bolts  having  the  Sellers1  thread  as  compared  with  bolts  having  the 
common  sharp  V  thread. 


1 

1 

W   ^  rS^ 

||| 

"o 

1 

|ll 

||| 

B 

2 

I-S-S 

|S| 

«~ 

| 

g  05 

| 

? 

fa 

sill 

|j| 

o 

11 

Is 

o 

11 

Sill 

ill! 

i|L 

£ 

* 

o"0^ 

o  * 

ft 

iz; 

o 

e 

Inch. 

Inch. 

i 

20 

28.3 

45.4 

I 

8 

14.1 

21.9 

A 

18 

23.1 

36.6 

1J 

7 

14.6 

22.7 

f 

16 

21.5 

33.9 

li 

7 

12.7 

19.7 

ft 

14 

20.9 

32.9 

If 

6 

14.1 

21.8 

13 

18.9 

29.7 

6 

12.4 

19.2 

A 

12 

17.8 

28.0 

l£ 

54 

124 

19.2 

11 

17.6 

27.5 

If 

5 

12.8 

19.8 

f 

10 

155 

24.2 

1£ 

5 

11.7 

18.1 

i 

9 

14.6 

22.3 

2 

4* 

124 

19.1 

The  data  of  this  table  may  be  approximately  summed  up  by 
the  statement  that  the  smaller  bolts,  with  the  Sellers  thread, 
have  about  a  quarter  more  strength,  the  medium  sized  ones  a 
sixth  more,  and  the  larger  ones  an  eighth  more  strength  to  resist 
tension  than  screws  having  an  ordinary  V  thread.  The  resist- 
ance to  torsion  of  screws  with  the  Sellers  thread  is  about  a  third,  a 
quarter,  and  &  fifth  greater  respectively,  than  those  with  a  V  thread. 

These  advantages  of  the  Sellers  thread  were  recognized  by  the 
board  of  engineers  referred  to,  and  they  reported  that  u  the 
board  unhesitatingly  recommends  it  as  a  standard  for  the  Navy." 
Mr.  Isherwood,  the  chief  of  the  Bureau  of  Steam  Engineering 
at  that  time,  wrote  to  the  Secretary  of  the  Navy,  and  said  that 
he  "  fully  agreed  with  the  conclusions  of  the  report."  Hon. 
Gideon  Welles,  at  that  time  Secretary  of  the  Navy,  then  issued 
the  following  order : 


63 

"  The  standard  for  the  dimensions  of  bolts  and  nuts,  as  deter- 
mined by  the  board,  is,  upon  your  (Isherwood's)  recommenda- 
tion, authorized  for  the  naval  service." 

Soon  after  its  organization  the  Master  Mechanics'  Association 
recommended  the  Sellers  or  Franklin  Institute  system  of  threads 
for  general  use  in  locomotive  construction,  and  in  1871  the  Car- 
Builders  recommended  it  for  cars. 

Unfortunately,  though,  when  this  was  done,  a  large  propor- 
tion of  the  members  of  the  two  associations  seemed  to  have  the 
impression  that  the  Sellers  system  consists  simply  in  a  standard 
for  the  number  of  threads  to  the  inch,  and  apparently  not  suffi- 
cient effort  has  been  made  to  impress  the  fact  on  the  minds  of 
those  who  have  the  control  of  such  matters  that  three  features 
are  essential  to  the  Sellers  system  : 

FIRST,  screws  must  have  a  given  number  of  threads  per  inch. 

SECOND,  the  threads  must  be  of  the  form  and  proportions  designated. 

THIRD,  the  diameters  of  the  screws  must  conform  to  the  sizes  specified. 

A  screw  which  does  not  conform  to  the  Sellers  system  in  all 
three  particulars  has  not  a  legitimate  Sellers  thread.  All  screws 
with  a  number  of  threads  per  inch  different  from  those  given  in 
the  preceding  table  do  not  agree  with  the  requirements  of  the 
Sellers  system.  But,  even  if  the  number  of  threads  per  inch  is 
right,  if  the  shape  of  the  thread  is  different  from  that  specified  it 
is  not  a  Sellers  screw.  It  is  just  as  much  an  illegitimate  or 
bastard  screw  if  the  thread  is  made  V  shaped  and  the  pitch 
right  as  though  the  pitch  was  wrong  and  the  shape  of  thread 
was  right. 

The  committee  wish  to  impress  upon  this  Association  that  a 
specific  diameter  of  the  screw  is  an  essential  feature  of  the  Sel- 
lers system.  A  screw  with  a  Sellers  thread  must  be  of  one  of  the 
diameters  given  in  the  table.  There  are  no  other  sizes  in  the 
system,  excepting  some  larger  than  those  given,  which  are  not 
used  in  car  construction.  There  is  no  such  thing,  for  example, 
as  a  Sellers  screw  f  and  ^  inch  in  diameter.  That  size  is  not 
recognized  and  has  no  existence  in  the  system,  and  if  a  screw  is 
made,  as  is  often  done,  |  inch  in  diameter  "  a  sixty-fourth  "  or  "  a 
thirty-second  large,"  it  ceases  to  be  a  Sellers  screw..  Uniformity 
in  diameter  is  as  essential  to  interchangeability  as  uniformity  in 
the  number  of  threads  per 'inch  or  the  shape  of  the  threads,  and 


64 

the  importance  of  maintaining  the  former  can  not  be  too  strongly 
urged  on  this  association.  Just  as  soon  as  the  practice  is  intro- 
duced of  making  screw  threads  "  over  size,"  or  a  thirty-second 
or  sixty-fourth  large,  iriterchangeability  of  bolts  and  nuts  becomes 
impossible.  If  the  Sellers  standard  is  adopted,  no  screws  should 
be  tolerated  which  are  a  fraction  of  an  inch  larger  or  smaller 
than  the  diameter  specified  for  that  system. 

The  committee  are  quite  well  aware  that  the  reason  given  for 
making  screws  over  size  is  that  round  iron  is  nearly  always  rolled 
larger  than  its  nominal  diameter,  and  that  it  is  impracticable  to 
cut  it  down  to  the  required  dimension  with  the  dies  used  in 
cutting  screws.  If  iron  is  over  size  there  will,  of  course,  be  this 
difficulty;  but  there  is  no  serious  trouble  in  getting  round  iron 
made  of  the  right  diameter.*  On  the  Erie  road  this  whole  subject 
was  thoroughly  investigated  by  Mr.  Chanute,  a  few  years  ago. 
He  then  found  that  manufacturers  were  furnishing  nearly  all 
iron  for  bolts  over  size,  and  that  the  company  was  then  consum- 
ing about  700,000  pounds  of  round  iron  for  bolts.  "  On  this," 
he  writes,  "  we  estimated  the  over-sizes  and  weights  to  be  not  less 
than  five  per  cent.,  making  35,000  Ibs.,  worth  at  three  cents  per 
pound  $1,050,  which  we  paid  for  more  than  we  ordered."  lie 
therefore  issued  the  following  order  : 

u  All  iron  and  steel  received  for  bolts  shall  be  carefully  inspected,  to 
make  sure  that  it  does  not  run  over  or  under  size,  and  bars  involving 
double  cutting,  or  too  small,  shall  be  rejected" 

This  order  has  been  in  force  for  several  years,  and  Mr.  Chanute 
has  informed  your  committee  that  there  is  no  practical  difficulty 
in  enforcing  it.  The  manufacturers  who  supplied  iron  to  the 
company,  were  first  notified  that  thereafter  no  iron  which  was 
over  size  would  be  accepted.  The  above  order  was  then  issued, 
and,  although  it  was  found  necessary  at  first  to  reject  a  few  lots 
received,  the  manufacturers  soon  "  grasped  "  the  idea,  and  since 
then  there  has  been  no  trouble,  excepting  to  inspect  the  iron  and 
reject  an  occasional  lot  for  not  conforming  to  the  proper  dimen- 
sions. It  will  thus  be  seen  that  not  only  does  the  use  of  over- 
size screws  make  interchangeability  impossible,  but  it  is  also  a 
source  of  additional  expense  to  a  railroad  company,  which  is  not 
to  be  despised.  There  is,  therefore,  every  reason  for  adopting 

*  See  reprinted  article  '  A  SCKEW-THREAD  PRIMEK,"  page  83,  et  seq. 


65 

the  Sellers  standard  sizes  of  screw  threads  for  all  screws  used  in 
car  construction. 

But,  while  the  form,  proportions,  and  dimensions  of  the  stand- 
ard screw  threads  were  as  definitely  fixed  by  Mr.  Sellers  and  the 
action  of  the  Franklin  Institute  as  it  is  possible  for  them  to  be, 
and  although  it  was  thus  made  plain  what  the  standard  screws 
should  be,  subsequent  experience  showed  that  it  was  not  so  easy 
as  it  appeared  to  make  them  conform  with  a  sufficient  degree  of 
precision  for  practical  purposes  to  the  requirements  laid  down  by 
Mr.  Sellers.  This  difficulty  was  very  well  described  by  Mr. 
Channte,  at  one  of  the  monthly  meetings  of  this  Association,  in 
New  York,  held  on  Dec.  18,  1879. 

That  gentleman  was  then  in  charge  of  the  machinery  depart- 
ment of  the  New  York,  Lake  Erie  &  Western  Eailroad.  The 
meeting  was  called  to  consider  "  The  standard  system  of  screw 
threads,  and  the  best  method  of  maintaining  exact  sizes  of  screws, 
so  that  bolts  and  nuts  may  be  interchangeable."  Mr.  Wm. 
Sellers,  the  originator  of  the  system  which  bears  his  name,  and 
the  manufacturers  of  taps  and  dies  were  invited  to  be  at  the 
meeting,  and  were  present.  Mr.  Chanute  then  said : 

"  In  1874  the  Sellers  system  was  adopted  on  the  Erie  road, 
and  a  set  of  standard  taps  and  dies  had  been  furnished  to  each 
of  the  shops  on  that  line,  which  as  they  wore  out  were  replaced 
by  others  made  from  the  originals  at  each  of  the  shops.  In  1870 
attention  was  called  to  the  fact  that  some  nuts  cut  at  one  shop 
would  not  fit  bolts  cut  at  others,  and  an  investigation  was  made. 
A  set  of  nuts  of  the  different  sizes  were  cut  at  each  of  the  shops, 
and  were  sent  to  Messrs.  Pratt  &  Whitney,  who  fitted  soft  plugs, 
made  of  Babbit  metal,  into  each  of  these  nuts.  These  were  ex- 
hibited on  the  table.  By  taking  at  random  a  plug  and  a  nut 
of  nominally  the  same  diameter,  it  was  found  that  the  one  would 
rarely  fit  the  other.  It  was  seen  that  not  only  were  the 
diameters  different,  but  in  many  cases  the  pitch  and  angle  of  the 
threads  had  been  altered  from  the  original  standard,  and  the  taps 
made  at  different  shops  did  not  conform  to  each  other.  Nuts 
were  taken  from  twenty-three  or  twenty-four  foreign  cars,  and 
these  not  only  were  unlike  their  own  screws,  but  were  also  unlike 
each  other.  This  was  the  cause  of  great  waste,,  detention,  and 
expense  in  making  repairs. 


66 

"  It  was  found,  moreover,  that  the  practice  had  generally 
obtained  of  making  taps  over  size,  so  that  all  bolts  above  f  inch 
in  diameter  were  fa  in.  and  the  smaller  bolts  ^  in.  over  size. 
Investigation  showed  that  the  company  was  paying  for  about 
35,000  Ibs.  of  iron  more  than  would  have  been  required  if  it  had 
been  furnished  of  exact  sizes.  Instructions  were  therefore 
issued  that  no  more  taps  and  dies  should  be  made  at  the  various 
shops,  and  since  then  these  tools  have  all  been  bought  from 
manufacturers  of  them,  at  considerably  less  cost  than  they  could 
be  made  for  in  the  company's  shops.  It  was  supposed  that  in 
this  way  absolute  uniformity  could  be  obtained.  In  order  to 
have  the  benefit  of  competition,  however,  taps  were  bought  of 
different  manufacturers.  It  was  found,  however,  that  some  of 
the  nuts  cut  with  taps  bought  of  one  manufacturer  could  not  be 
screwed  on  a  tap  made  by  another.  This  led  to  a  request  to  the 
manufacturers  to  furnish  sets  of  their  standard  screw  gauges, 
which  were  compared  with  the  standard  gauges  at  the  Brooklyn 
Navy  Yard.  To  their  surprise  it  was  found  that  the  gauges  did 
not  agree  with  each  other,  and  although  the  difference  was  not 
very  great,  it  was  sufficient  to  prevent  the  bolts  and  nuts,  made 
to  conform  to  them,  from  interchanging  with  each  other." 

After  Mr.  Chanute  had  made  this  statement,  Mr.  Sellers  said: 
"  The  remarks  lead  me  to  believe  that  the  difficulty  does  not 
exist  in  the  system  of  screw  threads  so  much  as  it  does  in  the 
matter  of  the  original  standard.  ...  It,  perhaps,  has  been  thirty 
years  since  I  first  used  what  we  supposed  were  standard  sizes  in 
our  works,  as  I  was  very  early  impressed  with  the  importance  of 
having  some  standard  to  which  we  might  refer  all  our  measures. 
There  was  no  one  making  standard  gauges  at  that  time,  except 
Mr.  Whitworth  of  Manchester,  England,  and  we  imported  a  full 
set.  They  were  very  nicely  fitted  up  —  so  nicely,  indeed,  that 
they  seemed  to  be  unsuited  for  the  work-shop,  and  I  devised  a  set 
of  inside  and  outside  calipers  for  work-shop  use,  and  used  the 
standard  gauges  merely  for  the  purpose  of  reference.  In  our 
innocence,  we  never  suspected  that  there  might  be,  practically, 
different  measurements  of  the  same  thing,  or  that  there  was  any 
difference  in  such  standard  measures  ;  and  we  might,  perhaps, 
have  gone  on  much  longer  in  that  blissful  state  of  ignorance,  if 
it  had  not  been  that  we  ordered  another  set  from  Mr.  Whitworth, 


67 

and  when  we  had  the  two  we  found  that  they  did  not  at  all  agree 
perfectly.  It  was  impossible  to  determine  which  was  right, 
without  going  into  a  very  laborious  investigation,  which  we 
could  not  think  of,  and  we  put  the  old  set  aside.  I  remember 
that  we  did  not  purchase  the  last  set  until  after  Mr.  "Whitworth 
had  written  his  paper  upon  contact  measurements,  and  we 
therefore  used  the  last  set,  thinking  that  it  would  be  more  exact." 

Subsequent  inquiry  elicited  the  fact  that  the  manufacturers  of 
taps  and  dies  had  been  working  to  different  standards.  Soon 
after  the  Sellers  standard  was  recommended  by  the  Franklin 
Institute,  a  number  of  sets  of  their  new  standard  screw-gauges 
were  made  by  Mr.  Fox.  One  of  these  sets  is  at  the  Brooklyn 
Navy  Yard,  and  others  were  bought  by  manufacturers  of  taps 
and  dies,  and  were  used  as  standards  to  which  the}7  worked,  while 
The  Pratt  &  Whitney  Company  undertook  to  work  to  what  they 
regarded  as  a  true  inch,  and  the  fraction  thereof.  As  neither  the 
inch  nor  the  gauges  were  certainly  known  to  be  correct,  it  is  not 
remarkable  that  the  bolts  and  nuts* cut  with  tools  made  by 
different  manufacturers  were  not  interchangeable. 

The  question  then  came  up,  which  was  right?  With  com- 
mendable zeal  The  Pratt  &  Whitney  Company  undertook  to  test 
the  matter  by  reference  to  the  most  reliable  standards  and 
measuring  instruments  in  the  country.  Like  Diogenes  with  his 
lamp,  in  search  of  an  honest  man,  this  company  went  to  and  fro 
in  the  land  in  search  of  a  true  inch,  a  true  foot,  or  a  true  yard. 
They  procured  from  different  sources  what  they  supposed  were 
the  most  reliable  standards  of  measurement,  and  found  that  none 
agreed.  They  had  the  same  standards  measured  by  what  were 
considered  the  most  reliable  measuring  machines  and  instruments 
in  the  country,  and  found  that  no  two  of  these  would  measure 
the  same  standard  alike. 

It  would  lengthen  out  this  report  —  already  too  long  —  to  an 
unreasonable  extent  to  detail  their  efforts  in  this  direction.  Let 
it  be  sufficient  to  say  that  the  results  of  their  investigations  led 
them  to  doubt  whether  there  was  any  final  standard  of  reference 
in  this  country,  or  any  instruments  for  measuring  and  sub-divid- 
ing the  standard,  if  it  existed,  which  could  be  relied  upon  to  give 
results  which  would  be  at  all  satisfactory.  Inasmuch  as  the 
matter  was  of  very  great  importance  to  that  company  in  the 


68 

manufacture,  not  only  of  taps  and  dies,  but  of  other  tools,  gauges, 
and  instruments  of  precision,  they  determined  to  go  to  the  bottom 
of  the  subject,  and  lay  a  foundation  against  which  no  wind  or 
wave  of  doubt  or  uncertainty  could  prevail.  Happily,  about 
this  time  this  company  was  brought  into  communication  with 
Prof.  "W.  A.  Rogers,  connected  with  the  Cambridge  Observatory, 
and  professor  of  Astronomy  at  Harvard  College,  who  was 
interested,  although  for  a  widely  different  purpose,  in  the  subject 
of  precise  measurements,  and  had  studied  it  here  and  in  Europe. 
He  was  satisfied  that  the  celebrated  Whitworth  measuring  ma- 
chine had  defects,  and  therefore  he  proposed  an  entirely  different 
system.  He  had  the  ideas,  and  The  Pratt  &  Whitney  Company 
had  the  means  and  the  skill  to  put  them  into  practice.  The 
astronomer  and  the  mechanic  therefore  cooperated,  and  the  for- 
mer supplied  the  plan  for  a  comparator,  or  measuring  machine, 
and  it  was  agreed  between  them  that  the  company  should  make 
two  of  them,  one  to  be  used  by  Professor  Rogers  in  his  scientific 
investigations  at  Cambridge,  and  the  other  The  Pratt  &  Whitney 
Company  would  use  in  connection  with  the  manufacture  of  tools 
for  minute  measurements,  gauges,  etc. 

The  company  also  procured  the  services  of  Mr.  George  M. 
Bond,  a  graduate  of  the  Stevens  Institute,  who  has  had  charge 
of  the  work  done  on  the  machine,  and  to  whom  much  of  the 
credit  is  due  for  the  results  attained.  Ever  since  your  committee 
was  first  appointed,  The  Pratt  &  Whitney  Company  has  been 
engaged  in  constructing  these  machines  and  doing  the  preliminary 
work  and  producing  the  plant  which  was  required  to  construct 
exact  screw  and  other  gauges. 

It  will  be  impossible  in  a  report  like  this  to  give  a  description 
of  the  methods  employed  to  secure  the  utmost  attainable  pre- 
cision, nor  of  the  construction  of  this  machine.  It  must  be  suffi- 
cient to  say  that  with  it  measurements  of  5^,-^  of  an  inch  can 
be  made  with  certainty.  To  give  an  idea  of  what  is  implied  by 
this,  let  it  be  supposed  that  a  person  should  take  a  pair  of  divid- 
ers and  lay  off  50,000  prick-marks  ^  of  an  inch  apart  in  a  straight 
line.  To  do  this  the  line  would  require  to  be  over  520  ft.  or  nearly 
a  tenth  of  a  mile  long.  Imagine  that  many  prick-marks  com- 
pressed into  the  space  of  1  inch,  and  you  have  an  imperfect  idea 


69 

of  the  minuteness  of  the  measurements  which  can  now  be  made 
by  The  Pratt  &  Whitney  Company. 

Doubtless  there  are  many  members  of  this  Association  who, 
like  the  members  of  this  committee,  when  they  undertook  the 
work  assigned  to  them,  if  asked  what  are  the  actual  standards  of 

C5 

measurement  in  this  country,  could  not  answer  such  an  inquiry. 
A  brief  statement  of  what  the  existing  standards  of  linear  meas- 
urements actually  are  may  therefore  be  interesting.  Like  many 
other  good  things,  we  have  inherited  these  from  Great  Britain. 
In  1834,  the  British  standards  were  destroyed  by  the  burning  of 
the  Parliament  buildings.  In  an  article  in  the  Franklin  Institute 
Journal  of  February,  1880,  by  Professor  Hilgard,  he  says  : 

"  The  actual  standard  of  length  used  in  this  country  was  a 
bronze  scale  of  82  in.,  subdivided  on  silver  to  tenths  of  inches, 
which  had  been  prepared  for  the  Coast  Survey  of  the  United 
States  by  Troughton  of  London.  The  36-in.  comprised  between 
the  27th  and  63d  inches,  found  equal  to  the  average  of  the  whole 
scale,  were  taken  as  the  standard  yard,  and  the  temperature  at 
which  this  was  considered  to  be  standard,  that  is  to  say  equal  to 
the  British  standard  yard,  was  presumed  to  be  62°  Fahr." 

The  Troughton  scale  was  made  before  the  destruction  of  the 
British  standards.  Since  then  the  latter  have  been  reproduced 
by  reference  to  all  the  accredited  standards  with  which  they 
had  originally  been  compared.  In  Clark's  "  Manual  for  Mechan- 
ical Engineers,"  it  is  said:  "The  present  British  standard  yard 
is  a  solid  square  bar  of  gun-metal,  kept  in  the  office  of  the  Ex- 
chequer at  Westminster,  38  in.  in  length,  1  in.  square,  at  the 
temperature  of  62°  Fahr.,  composed  (proportionally)  of  copper 
16  ounces,  tin  2J  ounces,  and  zinc  1  ounce.  Two  cylindrical 
holes  are  drilled  half  through  the  bar,  one  near  each  end,  and 
the  centers  of  these  holes  are  36  in.  or  3  it.  apart  —  the  length  of 
the  imperial  standard  yard." 

Since  the  British  standards  have  been  reproduced,  some  fifty 
copies  have  been  constructed  and  intercompared,  and  certain  of 
these  copies  have  been  sent  to  the  United  States.  According  to 
Professor  Hilgard,  recent  comparisons  have  shown  that  the 
Troughton  scale  is  0.00076  inch  in  the  yard  too  long.  He  says  : 
"  This  change,  though  sensible  in  operations  of  extreme  scientific 
precision,  is  really  of  no  consequence  in  ordinary  practice. 


70 

"  Extreme  accuracy  in  this  matter  is  beset  with  great  difficul- 
ties, for  in  addition  to  that  of  ascertaining  for  each  particular  bar 
the  rate  of  dilatation  by  temperature,  there  is  an  uncertainty  in 
regard  to  permanence  in  the  length  of  the  bars  themselves.  Of 
the  two  standard  yards  presented  to  the  United  States,  one  is  of 
bronze  and  the  other  of  Low  Moor  wrought  iron.  These  are 
found  to  have  changed  their  relative  length  by  0.00025  in.,  or 
1-400  of  an  inch  in  25  years,  the  bronze  bar  being  now  relatively 
shorter  by  that  amount." 

The  standard  bars  used  by  The  Pratt  &  Whitney  Company 
were  first  prepared  by  them,  and  were  graduated  by  Professor 
Rogers,  and  were  then  sent  to  Washington  to  be  compared  with 
the  standards  there.  Professor  Hilgard  reported  that  one  bar 
was  0.000053  inch  longer  than  the  imperial  yard,  and  another 
was  0.000036  inch  shorter  than  this  unit;*  the  mean  of  the  two 
bars  differs  from  the  imperial  yard  by  a  quantity  less  than  the 
certainty  with  which  such  comparisons  can  be  made,  viz.,  0.00001 
inch. 

After  having  a  bar  of  standard  length,  it  becomes  necessary  to 
subdivide  it  into  such  divisions  as  are  required  in  practical  use. 
Af  hardened  steel  six-inch  bar  was  thus  graduated  into  line 
measure,  and  is  the  one  which  is  chiefly  used  as  the  standard  for 
the  measurements  required  in  the  manufacture  of  screw  gauges. 
To  quote  from  a  paper  read  before  the  American  Society  of 
Mechanical  Engineers  by  Mr.  Bond,  this  bar  has  ruled  "  upon  its 
upper  polished  surface,  lines  ruled  four  separate  inches,  also  lines 
representing  —  counting  from  the  end  of  the  second  inch  —  the 
lengths  corresponding  to  the  bottom  diameters  or  '  tap  sizes '  of 
the  United  States  or  Franklin  Institute  standard  screw  threads, 
from  a  quarter  inch  to  four  inches. "f 

The  lines  or  graduations  on  this  bar  are  so  minute  that  it  re- 
quires good  eye-sight  to  see  them  with  the  naked  eye.  All  compar- 
isons of  these  divisions  are  made  by  observing  the  lines  through 
a  microscope.  The  bar  was  ruled  or  graduated  upon  a  dividing 
engine  made  by  the  American  Watch  Company  at  Waltham,  for 
Professor  Rogers. 

To  give  an  idea  of  the  difficulty  of  making  exact  measurements, 

*See  page  27.  Prof.  Rogers'  Report, 
t  Page  43  same  Report. 


71 

it  may  be  said  that  every  good  workman  knows  that  much  greater 
exactness  of  measurement  is  possible  with  two  rules  used  "  end 
to  end  "  than  can  be  made  by  drawing  aline  at  the  end  of  one  rule 
and  then  measuring  to  that  line  with  the  same  rule.  In  the 
same  way  a  pair  of  calipers  can  be  set  more  exactly  to  a  gauge 
than  to  the  lines  or  divisions  on  a  rule.  The  one  method  is 
called  "  end-measurement "  and  the  other  "  line-measurement." 
For  practical  use  the  line  graduations  on  the  six-inch  bar' referred 
to  must  be  reduced  to  end-measurement,  or,  in  other  words,  it 
must  be  possible  to  make  a  gauge  which,  measured  over  all,  will 
coincide  in  length  exactly  with  the  graduations  on  the  bar.  It 
will  be  impossible  to  explain  the  ingenious  way  in  which  this  is 
done  with  practically  absolute  precision,  and  also  the  way  in 
which  end-measurement  of  a  gauge,  or  of  one  bar,  can  be  com- 
pared with  the  graduations  on  another  bar  on  the  machine  de- 
scribed. This  can  be  done  quickly  and  with  the  utmost  pre- 
cision. Gauges  of  any  dimensions  indicated  on  the  bar  can  be 
made  and  verified,  and,  from  these,  measurements  can  be  taken  for 
practical  purposes. 

But  it  may  be  asked  in  what  way  are  car-builders  concerned, 
or  of  what  practical  value  are  such  extremely  minute  and  exact 
measurements  to  them?  In  reply  it  may  be  said  that  much 
smaller  measurements  than  persons  usually  suppose  are  of  im- 
portance in  ordinary  work,  and,  as  a  matter  of  fact,  workmen 
are  constantly  in  the  habit  of  measuring  with  calipers,  and  other 
means,  quantities  as  small  as  0.001  of  an  inch  or  even  much  less 
than  this.  This  is  illustrated  by  a  plug  and  ring  which  is  here 
exhibited.  The  former  is  £  inch  in  diameter,  and  tits  the  ring 
as  nearly  perfect  as  it  is  possible  to  make  it.  The  second  plug 
is  0.001  of  an  inch  smaller  than  the  first  one.  The  second  one 
fits  so  loosely  in  the  ring  that  you  can  feel  it  shake.  A  good 
machinist  in  fitting  the  pins  in  a  link  motion  can  easily  discern  a 
difference  of  much  less  than  0.001  inch  in  the  diameter  of  the  pins 
or  their  bearings.  If  the  latter  are  of  the  right  size  and  some  of 
the  pins  are  that  much  too  large,  interchangeability  will  be  im- 
possible. The  same  thing  is  true  of  screws  and  nuts.  To  illus- 
trate this,  a  |  bolt  and  nut  were  shown,  the  two  being  an  example 
of  an  ordinary  good  fit.  Another  bolt  -5^-$  smaller  in  diameter 


72 

was  also  exhibited.  The  nut  was  so  loose  on  the  latter  that  any 
good  mechanic  would  pronounce  it  a  bad  fit  and  a  bad  job.  It 
will  thus  be  seen  that  in  practice  a  very  considerable  amount  of 
precision  is  required  in  order  to  secure  good  workmanship.  As 
a  matter  of  fact,  there  are  no  serious  difficulties  in  maintaining 
such  a  degree  of  precision  in  practice  if  there  only  is  some  stand- 
ard to  work  to. 

The  results  of  the  investigations  of  Mr.  Chanute  on  the  Erie 
road  showed  what  occurs  when  taps  and  dies  are  made  nominally 
of  the  Sellers  system,  but  with  no  common  standard  of  measure- 
ment. To  maintain  a  system  of  screw  threads  which  will  be 
interchangeable  it  is  essential  that  they  be  made  to.  some  common 
and  exact  standard  of  measurement.  The  uncertainties  of  two- 
foot  rules  are  too  great  to  maintain  an  interchangeable  standard, 
when  as  much  precision  is  required  as  is  needed  in  screws.  If 
the  shops  and  manufacturers  have  standards  of  measurement 
which  do  not  agree,  the  screws  made  from  them  will,  of  course, 
not  be  alike.  It  is  essential,  therefore,  that  there  should  be  a 
uniformity  in  the  standards.  This  it  is  extremely  difficult  to 
bring  about,  and  unless  the  standard  proposed  is  as  near  right  as 
it  can  be  made  it  will  be  impossible  to  secure  its  general  adop- 
tion. People  object  to  conforming  to  what  they  know  is  not 
right,  and  the  person  who  can  say  "  My  standard  is  right  and  yours 
is  wrong,''  has  an  unanswerable  argument  in  favor  of  his  practice. 

Besides  being  important  that  standards  should  be  exactly  right, 
it  is  essential  that  it  should  be  possible  to  reproduce  them  to  any 
extent  that  is  desirable,  even  though  the  original  was  lost.  This 
The  Pratt  &  Whitney  Company  have  supplied  the  means  of 
doing. 

It  may  be  said  also  that  even  if  a  degree  of  precision  at  all 
approximating  to  that  which  has  been  arrived  at  by  The  Pratt  & 
Whitney  Company  could  be  attained  in  the  manufacture  of 
screws  and  nuts  it  could  not  be  kept  up  on  account  of  the  wear 
to  which  taps  are  necessarily  subjected. 

Messrs.  Hoopes  &  Townsend,  of  Philadelphia,  have  informed 
your  committee  that  the  record  taken  from  their  books  shows 
that  with  a  £  in.  tap  they  have  tapped  18,800  cold-pressed  nuts 
without  any  difference  being  perceptible  in  the  size  of  the  nuts. 


73 

With  a  |  tap  they  have  cut  16,260,  and  with  a  J  in.  tap  18,000 
without  perceptibly  changing  the  size  of  the  nuts.* 

It  may  be  thought,  though,  that  accuracy  and  interchange- 
ability  of  the  Sellers  system  of  screws  can  be  maintained  if  they 
are  only  made  of  the  right  pitch  and  of  the  specified  diameter  on 
the  outside  and  at  the  root  of  the  thread ;  if  the  tool  for  cut- 
ting the  latter  is  made  of  the  proper  form,  and  if  the  thread  is 
cut  so  that  the  flat  at  the  point  and  root  are  equal.  This  is  true 
if  all  these  operations  are  performed  with  the  requisite  degree  of 
precision.  It  would  be  interesting  to  describe  all  the  processes, 
the  tools  and  instruments  which  are  used  by  The  Pratt  &  Whit- 
ney Company  in  making  taps,  dies,  and  screw  gauges,  but  to  do 
so  would  increase  this  already  extended  report  to  inadmissible 
dimensions.  A  brief  general  description  is  all  that  can  be  given. 

The  first  step  in  making  a  tap  or  screw  gauge  is  to  turn  a  bar 
of  steel  to  the  exact  diameter  of  the  outside  of  the  screw.  Then, 
one  end  of  the  portion  on  which  the  thread  is  to  be  cut  is 
turned  down  to  the  diameter  of  the  screw  at  the  root  of  the  thread. 

On  the  exactness  of  this  first  operation  the  precision  of  the 
ultimate  size  of  the  gauge  will  depend.  It  is  therefore  essen- 
tial to  be  able  to  measure  exactly  these  two  diameters.  The 
next  step  is  to  cut  the  thread.  To  do  this  a  tool  must  be  ground 
which  will  cut  a  thread  whose  sides  will  have  an  angle  of  exactly 
60°  to  each  other.  An  amount  equal  to  one-eighth  of  the  pitch 
must  be  taken  off  the  point  of  the  tool,  the  fiat  portion  being  true 
to  the  sides  of  the  thread.  To  make  a  true  thread  the  tool  must 
then  be  set  so  that  its  center  line  will  be  square  with  the  axis  of 
the  screw.  In  order  to  be  able  to  do  this  the  sides  of  the  tool 
are  ground  so  as  to  be  true  parallel  planes,  and  the  parts  which 
cut  the  sides  of  the  thread  are  ground  so  as  to  be  true  with  the 
sides  of  the  tool  and  at  an  angle  of  60°  to  each  other.  It  can 
then  be  set  true  in  a  lathe  writh  a  try-square  bearing  against  its 
sides,  or  against  the  plane  end  of  the  headstock  of  the  lathe.  What 
adds  to  the  difficulty,  though,  is  the  fact  that  a  cutting  tool  of  this 
kind  does  not  stand  vertically,  but  at  an  angle  of  20°  to  a  per- 
pendicular line,  while  the. top  surface  is  horizontal.  Now  if  the 
portions  of  the  tool  which  conform  to  the  sides  of  the  thread  were 

*  For  results  even  more  remarkable,  see  Lecture  on  Standards  of  Length  as  Ajyplied  to 
Gauge  Dimensions. 


74 

ground  with  an  angle  of  60°  to  each  other,  the  edges  of  a  plane 
which  intersects  these  sides  at  an  angle  of  more  or  less  than  90° 
would  not  be  inclined  at  an  angle  of  60°  to  each  other.  For  this 
reason  the  tool  must  be  ground  at  an  angle  of  somewhat  greater 
than  60°,  so  that  the  cutting  edges  formed  by  the  intersection  of 
the  flat  top  surface  and  the  inclined  edges  of  the  tool  will  be 
exactly  60°.* 

It  would  be  impossible,  without  elaborate  illustrations,  to  give 
a  description  of  the  delicate  instrument  which  is  used  to  measure 
the  exact  amount  that  should  be  taken  off  the  point  of  the  tool 
for  cutting  threads  of  various  sizes.  It  must  be  sufficient  to  say 
that  this,  too,  is  done  with  the  highest  degree  of  precision,  f 

These  processes  and  appliances  are  required  to  make  a  turning- 
tool  of  the  exact  shape  and  size  to  cut  the  threads  of  screw 
gauges.  With  such  a  tool,  then,  and  a  blank  cylindrical  end  for 
a  gauge,  such  as  has  been  described,  it  would  seem  that  by  cut- 
ting the  thread  so  that  the  point  of  the  tool  would  just  touch 
that  part  of  the  blank  which  has  been  turned  down  to  the  size 
of  the  screw  at  the  root  of  the  thread,  the  screw  must  be  exactly 
of  the  right  size.  If,  as  has  been  said,  all  the  work  described  has 
been  done  with  absolute  precision,  such  will  be  the  case ;  but 
in  order  to  verify  it,  the  same  tool  used  for  cutting  the  thread  is 
put  into  a  planer  or  shaping  machine,  and  a  template  is  cut  with 
it  out  of  a  thin  piece  of  steel.  The  space  cut  out  of  the  steel 
plate  will,  of  course,  be  an  exact  duplicate  of  the  space  between 
the  threads.  As  the  space  between  the  threads  should  be  an 
exact  counterpart  of  the  thread  itself,  the  latter  can  be  measured 
by  the  template,  and  if  they  are  exactly  alike,  it  will  indicate  that 
all  the  operations  have  been  performed  with  the  required  preci- 
sion. If  so,  the  screw  thus  made  supplies  a  true  gauge  to  work 
to.  It  should  be  kept  in  mind  that  the  sides  of  the  threads  of  a 
screw  are,  or  should  be,  the  actual  bearing  surfaces,  and  that  in 
making  taps  and  dies,  the  threads  should  be  measured  over  the 
sides.  With  such  a  gauge  as  will  be  supplied  by  the  screw 
described,  it  is  an  easy  matter  to  set  an  ordinary  pair  of  calipers 
over  the  sides  of  the  threads,  and  then  reproduce  that  size  in  any 
number  of  other  screws  or  taps.  A  skillful  tool-maker  will  meas- 

*  The  "  clearance"  angle  being  20%  the  actual  angle  between  the  sides  of  the  threading  tool  is 
t  See  Lecture,  Standards  of  Length  as  applied  to  Gauge  Dimensions, 


75 

tire  with  ordinary  calipers  to  within  YrrJuT  of  an  inch,  provided 
he  has  a  correct  gauge  to  set  his  calipers  by.  Experience  has 
shown  that  with  a  gauge  of  the  kind  described  to  work  from,  a 
very  high  degree  of  precision  can  be  attained ;  but  it  was  also 
found  that  it  is  always  necessary  to  make  an  allowance  for  the 
wear  of  the  cutting  tool  which  occurred  when  first  used,  and 
therefore  to  make  it  somewhat  larger  than  the  actual  size  of  the 
thread. 

But  there  is  still  another  difficulty  with  screw  gauges.  If  they 
are  made  as  described,  the  steel  must  of  course  be  soft,  and  a 
very  little  use  would  soon  destroy  their  accuracy.  It  is  there- 
fore requisite  that  working  gauges  should  be  hardened.  The 
process  of  doing  so,  however,  changes  their  form  and  dimensions 
slightly,  so  as  to  impair  their  accuracy.  To  get  over  this  diffi- 
culty, hardened  gauges  are  made  somewhat  larger  than  the  stand- 
ard size.  The  Pratt  &  Whitney  Company  have  devised  a  plan 
to  grind  these  gauges,  after  they  are  hardened,  to  the  exact  size, 
form  and  pitch.  To  do  this  the  gauges  are  put  into  a  lathe  and 
a  rapidly  revolving  steel  disc  or  wheel  is  attached  to  the  tool- 
holder  which  is  moved  by  the  lead  screw,  the  pitch  of  which  con- 
forms exactly  to  that  of  the  screw  of  the  gauge.  Diamond  dust 
is  used  on  this  disc  for  grinding  the  hardened  threads,  and  the 
exact  size  is  reproduced  from  a  soft  gauge,  whose  dimensions 
have  not  been  changed  by  hardening. 

For  the  most  exact  standards  of  reference,  The  Pratt  &  Whit- 
ney Company  recommends  the  unhardened  gauges.  For  stan- 
dards of  reference  which  must  be  oftener  used,  and  where  a  high 
degree  of  precision  is  also  required,  the  hardened  and  ground 
gauges  are  recommended. 

They  will  also  furnish  another  kind  which  are  hardened  but 
not  ground,  to  be  used  in  the  shop  as  reference  gauges  and  which 
are  correct  enough  for  practical  purposes.*  Specimens  of  all  these 
kinds  are  submitted  with  the  report. 

It  should  be  clearly  understood  that  none  of  these  reference 
gauges  are  intended  for  shop  use,  and  that  if  subjected  to  much 
wear  their  accuracy  will  soon  be  destroyed.  The  size  of  new 

*  These  gauges,  hardened  and  not  ground,  are  within  a  limit  of  1-10,000  of  an  inch,  measured 
in  the  anglo  of  the  thread. 

See  page  87.    Article,  A  SCREW-THREAD  PRIMER. 


76 

taps  may  be  tested  by  them,  and  if  of  the  correct  size,  a  few 
nuts  may  be  cut  with  the  new  taps,  and  these  be  used  as  shop 
gauges  by  the  workmen.  As  these  wear  they  can  be  replaced 
with  new  nuts  cut  with  other  new  taps. 

The  external  gauges,  it  will  be  seen,  are  made  adjustable. 
The  internal  gauge  or  plug  is  the  real  guide  to  work  from  and 
the  former  can  always  be  set  from  the  latter.  The  committee 
finds  that  there  is  some  difference  of  opinion  among  those  having 
most  knowledge  of  the  subject  with  reference  to  the  need'of  the 
external  gauges.  Some  hold  that  a  correct  internal  or  plug  screw 
gauge  is  sufficient  to  test  the  size  of  a  tap,  and  then  the  nuts, 
already  referred  to,  will  answer  for  working  gauges  to  maintain 
standard  sizes  in  the  shop. 

Complete  sets  of  gauges  like  samples  here  shown  can  be  fur- 
nished by  The  Pratt  &  Whitney  Company  in  a  few  weeks  or 
months,  and  the  committee  think  that  the  master  car-builders,  and 
all  who  have  occasion  to  use  screws,  may  be  congratulated  that 
standard  screw  gauges  can  now  be  procured,  made  with  a  degree 
of  precision  which  has  never  been  attained  heretofore,  and  that 
this  has  largely  been  due  to  the  agitation  of  the.  subject  by  this 
Association.  It  is  worthy  of  note  that  a  remedy  for  the  evil  com- 
plained of  by  master  ^car-builders,  that  nuts  made  by  some  firms 
or  at  some  shops  would  not  screw  on  bolts  made  at  others,  at 
first  baffled  the  ability  of  the  most  prominent  manufacturers  of 
tools  of  precision  in  the  country,  and  that  to  provide  an  adequate 
remedy  it  was  necessary  to  secure  the  assistance  of  the  highest 
scientific  ability  in  the  country,  which  was  supplied  through  the 
co-operation  of  the  Professor  of  Astronomy  of  the  oldest  and 
most  noted  institution  of  learning  in  the  land.  The  man  of  sci- 
ence turned  his  attention  from  the  planets  and  the  measurement 
of  distances  counted  by  millions  of  miles,  to  listen  to  the  impre- 
cation, perhaps,  of  the  humble  car-repairer  lying  on  his  back  and 
swearing  because  a  |  nut  —  "a  leetle  small"  — will  not  screw  on 
a  bolt  a  "  trifle  large."  It  is  a  striking  example  of  the  assistance 
which  science  can  give  in  conducting  the  "  practical "  affairs  in 
life. 

In  conclusion,  the  committee  would  recommend  that  this  Asso- 
ciation in  conjunction  with  the  Master  Mechanics'  Association,  pro- 
cure a  set  of  the  unhardened  gauges  manufactured  by  The  Pratt 


77 

&  Whitney  Company,  and  that  these  be  kept  among  the  archives 
of  one  or  the  other  of  the  associations,  as  the  standard  of  measure- 
ment of  screw  threads  and  for  ultimate  reference  in  case  of  need. 
They  would  also  suggest  the  adoption  of  the  following  resolu- 
tions : 

"That  this  Association  deprecates  the  use  of  screws  larger  or  smaller  in 
diameter  by  a  small  fraction  of  an  inch  than  the  sizes  specified  for  the  Sellers 
or  Franklin  Institute  system,  and  that  all  its  members  are  urged  to  abandon 
entirely  the  use  of  over  or  under  size  screws. 

"  That  the  thanks  of  this  Association  be  voted  to  The  Pratt  &  Whitney  Com- 
pany for  the  intelligence,  liberality,  and  enterprise  shown  in  their  efforts  to 
establish  a  system  of  accurate  gauges  for  screws  and  for  tools  for  precise 
measurement. 

"  That  the  committee  which  prepared  this  report  be  instructed  to  send  a  copy 
of  it,  with  a  suitable  circular  calling  attention  to  the  importance  of  adopting 
the  correct  standard  Sellers  system  of  screw  threads,  to  the  presidents,  mana- 
gers, superintendents  and  master  car-builders  of  the  United  States,  Canada,  and 
Mexico,  and  that  when  the  committee  has  performed  that  duty  it  be  discharged." 

M.  N.  FORNEY. 

The  above  report  was  received  and  its  concluding  resolutions 
were  adopted  by  the  Association,  with  an  amendment  instructing 
the  committee  to  procure  a  standard  two-feet  rule. 


[The  set  of  unhardened  gauges  representing  the  Sellers  or  United  States  Stand- 
ard thread  for  sizes  ^  in.  to  2  inches  inclusive,  referred  to  in  the  foregoing 
report,  was  delivered  to  the  Master  Car-Builders'  Association  at  their  adjourned 
meeting  at  Niagara  Falls,  October,  1882. 

The  24  in.  standard,  which  includes  both  line  and  end-measure,  after  having 
been  graduated  and  rigidly  investigated  by  Professor  Rogers,  —  a  work  cover- 
ing a  period  of  over  a  year  —  was  delivered  to  the  Association  at  their  annual 
convention  held  in  Saratoga,  June,  1884.] 


As  a  matter  of  interest  and  for  reference,  the  Report  of  the 
Special  Committee  appointed  by  the  Franklin  Institute  to  investi- 
gate the  Screw-Thread  question  as  applied  to  Bolts  and  Nuts,  is 
here  appended : 


78 

"  Extract  from  the  Proceedings  c>f  a  Stated  Hating  of  the  Franklin 
Institute  of  the  State  of  Pennsylvania  for  the  Promotion  of  the 
Mechanic  Arts,  held  December  15,  1864. 

"  The  Special  Committee  appointed  by  the  Franklin  Institute, 
April  21,  1864,  to  investigate  the  question  of  the  proper  system 
of  Screw  Threads,  Bolt-heads,  and  Nuts,  to  be  recommended  by 
the  Institute  for  general  adoption  by  American  Engineers, 

REPORT, 

"That  in  the  course  of  their  investigations  they  have  become 
more  deeply  impressed  with  the  necessity  of  some  acknowledged 
standard,  the  varieties  of  threads  in  use  being  much  greater  than 
they  had  supposed  possible;  in  fact,  the  difficulty  of  obtaining 
the  exact  pitch  of  a  thread  not  a  multiple  or  sub-multiple  of  the 
inch  measure  is  sometimes  a  matter  of  extreme  embarrassment. 

"  Such  a  state  of  things  must  evidently  be  prejudicial  to  the 
best  interests  of  the  whole  country,  a  great  and  unnecessary 
waste  is  its  certain  consequence  ;  for  not  only  must  the  various 
parts  of  new  machinery  be  adjusted  to  each  other  in  place  of 
being  interchangeable,  but  no  adequate  provision  can  be  made 
for  repairs,  and  a  costly  variety  of  screwing  apparatus  becomes  a 
necessity.  It  may  reasonably  be  hoped  that  should  a  uniformity 
of  practice  result  from  the  efforts  and  investigations  now  under- 
taken, the  advantages  flowing  from  it  will  be  so  manifest  as  to 
induce  reform  in  other  particulars  of  scarcely  less  importance. 

"  Your  committee  have  held  numerous  meetings  for  the  purpose 
of  considering  the  various  conditions  required  in  any  system 
which  they  could  recommend  for  adoption.  Strength,  durability, 
with  reference  to  wear  from  constant  use  and  ease  of  construc- 
tion, would  seem  to  be  the  principal  requisites  in  any  general 
system ;  for  although  in  many  cases,  as,  for  instance,  when  a 
square  thread  is  used,  the  strength  of  the  thread  and  bolt  are 
both  sacrificed  for  the  sake  of  securing  some  other  advantage,  yet 
all  such  have  been  considered  as  special  cases,  not  affecting  the 
general  inquiry.  With  this  in  view,  your  Committee  decided 
that  threads  having  their  sides  at  an  angle  to  each  other  must 
necessarily  more  nearly  fulfill  the  first  condition  than  any  other 
form  ;  but  what  this  angle  should  be  must  be  governed  by  a  vari- 


79 

ety  of  considerations,  for  it  is  clear  that  if  the  two  sides  start 
from  the  same  point  at  the  top,  the  greater  the  angle  contained 
between  them  the  greater  will  be  the  strength  of  the  bolt ;  on 
the  other  hand,  the  greater  this  angle,  supposing  the  apex  of  the 
thread  to  be  over  the  center  of  its  base,  the  greater  will  be  the 
tendency  to  burst  the  nut,  and  the  greater  the  friction  between 
the  nnt  and  the  bolt,  so  that  if  carried  to  excess  the  bolt  would 
be  broken  by  torsion  al  strain  rather  than  by  a  strain  in  the  direc- 
tion of  its  length.  If,  however,  we  should  make  one  side  of  the 
thread  perpendicular  to  the  axis  of  the  bolt,  and  the  other  at  an 
angle  to  the  first,  we  should  obtain  the  greatest  amount  of 
strength,  together  with  the  least  frictional  resistance ;  but  we 
should  have  a  thread  only  suitable  for  supporting  strains  in  one 
direction,  and  constant  care  would  be  requisite  to  cut  the  thread 
in  the  nut  in  the  proper  direction  to  correspond  with  the  bolt. 
We  have  consequently  classed  this  form  as  exceptional,  and 
decided  that  the  two  sides  should  be  at  an  angle  to  each  other 
and  form  equal  angles  with  the  base. 

"  The  general  form  of  the  thread  having  been  determined  upon 
the  above  considerations,  the  angle  which  the  sides  should  bear 
to  each  other  has  been  fixed  at  60°,  not  only  because  this  seems 
to  fulfill  the  conditions  of  least  frictional  resistance,  combined 
with  the  greatest  strength,  but  because  it  is  an  angle  more  readily 
obtained  than  any  other,  and  it  is  also  in  more  general  use.  As 
this  form  is  in  common  use  almost  to  the  exclusion  of  any  other, 
your  Committee  have  carefully  weighed  its  ad  vantages  and  disad- 
vantages before  deciding  to  recommend  any  modification  of  it. 
It  cannot  be  doubted  that  the  sharp  thread  offers  us  the  simplest 
form,  and  that  its  general  adoption  would  require  no  special  tools 
for  its  construction,  but  its  liability  to  accident,  always  great, 
becomes  a  serious  matter  upon  large  bolts,  whilst  the  small 
amount  of  strength  at  the  sharp  top  is  a  strong  inducement  to 
sacrifice  some  of  it  for  the  sake  of  better  protection  to  the  remain- 
der ;  when  this  conclusion  is  reached,  it  is  at  once  evident  a  cor- 
responding space  may  be  filled  up  in  the  bottom  of  the  thread, 
and  thus  give  an  increased  strength  to  the  bolt,  which  may  com- 
pensate for  the  reduction  in  strength  and  wearing  surface  upon 
the  thread.  It  is  also  clear  that  such  a  modification,  by  avoiding 
the  fine  points  and  angles  in  the  tools  of  construction,  will 


80 

increase  their  durability ;  all  of  which  being  admitted,  the  ques- 
tion comes  up,  What  form  shall  be  given  to  the  top  and  bottom 
of  the  thread?  for  it  is  evident  one  should  be  the  converse  of  the 
other.  It  being  admitted  that  the  sharp  thread  can  be  made 
interchangeable  more  readily  than  any  other,  it  is  clear  that  this 
advantage  would  not  be  impaired  if  we  should  stop  cutting  out 
the  space  before  we  had  made  the  thread  full  or  sharp,  but  to  give 
the  same  shape  at  the  bottom  of  the  thread  would  require  that  a 
similar  quantity  should  be  taken  off  the  point  of  the  cutting  tool, 
thus  necessitating  the  use  of  some  instrument  capable  of  measur- 
ing the  required  amount;  but  when  this  is  done  the  thread,  hav- 
ing a  flat  top  and  bottom,  can  be  quite  as  readily  formed  as  if  it 
were  sharp.  A  very  slight  examination  sufficed  to  satisfy  us 
that,  in  point  of  construction,  the  rounded  top  and  bottom  pre- 
sents much  greater  difficulties ;  in  fact,  all  taps  and  screws  that 
are  chased  or  cut  in  a  lathe  required  to  be  finished  or  rounded  by 
a  second  process.  As  the  radius  of  the  curve  to  form  this  must 
vary  for  every  thread,  it  will  be  impossible  to  make  one  guage  to 
answer  for  all  sizes,  and  very  difficult,  in  fact  impossible,  without 
special  tools,  to  shape  it  correctly  for  one. 

"  Your  Committee  are  of  opinion  that  the  introduction  of  a 
uniform  system  would  be  greatly  facilitated  by  the  adoption  of 
such  a  form  of  thread  as  would  enable  any  intelligent  mechanic 
to  construct  it  without  any  special  tools,  or,  if  any  are  necessary, 
that  they  shall  be  as  few  and  as  simple  as  possible,  so  that 
although  the  round  top  and  bottom  presents  some  advantages 
when  it  is  perfectly  made,  as  increased  strength  to  the  thread  and 
the  best  form  to  the  cutting  tools,  yet  we  have  considered  that 
these  are  more  than  compensated  by  ease  of  construction,  the 
certainty  of  fit  and  increased  wearing  surface  offered  by  the  flat 
top  and  bottom,  and,  therefore,  recommend  its  adoption.  The 
amount  of  flat  to  be  taken  off  should  be  as  small  as  possible,  and 
only  sufficient  to  protect  the  thread ;  for  this  purpose  one-eighth 
of  the  pitch  would  seem  to  be  ample,  and  this  will  leave  three- 
fourths  of  the  pitch  for  bearing  surface.  The  considerations  gov- 
erning the  pitch  are  so  various  that  their  discussion  has  consumed 
much  time. 

"  As  in  every  instance  the  threads  now  in  use  are  stronger  than 
their  bolts,  it  became  a  question  whether  a  finer  scale  would  not 


81 


be  an  advantage.  It  is  possible  that  if  the  use  of  the  screw- 
thread  was  confined  to  wrought-iron  or  brass,  such  a  conclusion 
might  have  been  reached ;  but  as  cast-iron  enters  so  largely  into 
all  engineering  work,  it  was  believed  finer  threads  than  those  in 
general  use  might  not  be  found  an  improvement,  particularly 
when  it  was  considered  that,  so  far  as  the  vertical  height  of  thread 
and  strength  of  bolt  are  concerned,  the  adoption  of  a  flat  top  and 
bottom  thread  was  equivalent  to  decreasing  the  pitch  of  a  sharp 
thread  25  per  cent.,  or,  what  is  the  same  thing,  increasing  the 
number  of  threads  per  inch  33  per  cent.  If  finer  threads  were 
adopted  they  would  require  also  greater  exactitude  than  at  pres- 
ent exists  in  the  machinery  of  construction,  to  avoid  the  liability 
of  over-riding,  and  the  wearing  surface  would  be  diminished  ; 
moreover,  we  are  of  opinion  that  the  average  practice  of  the 
mechanical  world  would  probably  be  found  better  adapted  to  the 
general  want  than  any  proportions  founded  upon  theory  alone. 

"  We  have  taken  some  pains  to  ascertain  what  the  proportions 
in  use  are,  and  submit  the  following,  as  being  in  our  judgment  a 
fair  average,  viz : 


Diameter  of  Bolt, 
No.  threads  per  in 


Diameter  of  Bolt, 
No.  threads  per  in, 


#    5-16 


20     18 

I 

*%\4X 


16 


7-16 


14 


y* 


13 


9-16    % 


12     11 


3% 


10 


2% 


6 


4%\    5 


5* 


2% 


2% 


"  The  proportions  for  bolt-heads  and  nuts,  as  given  in  most  of 
our  books  of  reference,  are  believed  to  be  larger  than  necessary, 
and  all  are  tabulated,  necessitating  constant  reference.  A  simple 
formula  would  be  more  convenient,  and  would  probably  induce 
a  uniform  practice ;  but  as  most  of  the  sizes  in  common  use  are 
made  by  machinery,  and  also  by  hand,  it  is  believed  the  bolt-head 
and  nut  for  finished  work  should  be  made  somewhat  smaller  than 
for  rough,  to  avoid  the  confusion  that  would  ensue,  if  the  neces- 
sary allowance  for  dressing  should  be  made  upon  work  intended 
for  finishing. 

"  In  conclusion,  therefore,  your  Committee  offer  the  following  : 
"  Resolved,  That  the  Franklin  Institute  of  the  State  of  Penn- 
sylvania  recommend,   for  general  adoption    by  American  engi- 
neers, the  following  forms  and  proportions  for  screw-threads,. bolt- 
heads,  and  nuts,  viz. : 


82 


"  That  screw-threads  shall  be  formed  with  straight  sides  at  an 
angle  to  each  other  of  60°,  having  a  flat  surface  at  the  top  and 
bottom  equal  to  one-eighth  of  the  pitch.  The  pitches  shall  be 
as  follows,  viz.  : 


Diameter  of  Bolt, 
No.  threads  per  in 


Diameter  of  Bolt, 
No.  threads  per  in 


5-16    % 
20  i  18  |  16 

^__^_ 

4 


7-16 

14 


13 


zy, 


9-16 
18 


11 


10 


8*     3 


1 

ojT 

4   |4M   4% 


2% 


6    I    6 

5  ;5^ 


2% 


5    |    5 


2% 


"  The  distance  between  the  parallel  sides  of  a  bolt-head  and 
nut,  for  a  rough  bolt,  shall  be  equal  to  one  and  a  half  diameters 
of  the  bolt,  plus  one-eighth  of  an  inch.  The  thickness  of  the 
heads,  for  a  rough  bolt,  shall  be  equal  to  one-half  the  distance 
between  its  parallel  sides.  The  thickness  of  the  nut  shall  be 
equal  to  the  diameter  of  the  bolt.  The  thickness  of  the  head, 
for  a  finished  bolt,  shall  be  equal  to  the  thickness  of  the  nut. 
The  distance  between  the  parallel  sides  of  a  bolt-head  and  nut, 
and  the  thickness  of  the  nut,  shall  be  one-sixteenth  of  an  inch 
less  for  finished  work  than  for  rough. 

"  Resolved,  That  a  copy  of  these  resolutions  be  forwarded  to 
the  Quartermaster-General,  Chief  of  the  Bureau  of  Steam  Engi- 
neering of  the  Navy,  and  the  Chiefs  of  Ordnance  for  the  Army 
and  Navy,  and  Chiefs  of  the  Engineer  and  Military  R.  R.  Corps, 
and  the  Superintendent  and  M.  M.  of  R.  R.  Companies,  request- 
ing them  to  use  their  influence  to  promote  the  adoption  of  a  uni- 
form system  of  screw-threads,  bolt-heads,  and  nuts,  by  requiring 
all  builders  under  any  new  contracts  to  conform  to  the  propor- 
tions recommended. 

"  Resolved,  That  a  copy  of  these  resolutions  be  also  sent  to  all 
Mechanical  and  Engineering  Associations  or  Institutes,  and  the 
principal  machine  and  engine  shops  in  the  country,  with  a  request 
that  they  will  use  their  influence  in  the  proposed  system. 

^  Kesolued,  That  this  Committee  be  now  discharged." 

"WM.  B.  BEMENT,  Firm  of  Bemenl  £  Dougherty. 

C.  T.  PARRY,  Supt.  Baldwin's  Locomotive  Works. 
J.  YAUGHAN  MERRICK,  Firm  of  Merrick  &  /Sons. 

^JoHN  H.  TOWNE,  Firm  of  I.  P.  Morris,  Towne  &  Co. 

COLEMAN  SELLERS,  Eng.   Wm.  Sellers  &  Co. 

H.  BARTOL,  Supt.  Southwark  Foundry. 

EDWARD  LONGSTRETH,  Foreman  Baldwin's  Locomotive  Works. 

JAMES  MOORE,  Firm  of  Matthews  &  Moore. 

WM.  SELLERS,  Firm  of  Wm.  Sellers  &  Co. 

ALGERNON  HOBERTS,  Of  the  Pencoyd  Iron  Works" 


[REPRINTED  FROM  THE  R.  R.   GAZETTE,   JULY  20,  1883.] 

A  SCREW-THREAD  PRIMER. 


Notwithstanding  all  the  discussion  of  this  subject,  and  all  that 
has  been  written  about  it,  there  are  still  many  persons  whose 
duties  require  that  they  should  know  all  about  the  standard 
system  of  screw-threads,  but  who  are  nevertheless  in  almost  com- 
plete ignorance  of  what  has  been  done,  or  of  what  may  be  called 
the  present  status  of  the  question.  It  must  be  admitted  that  the 
information  which  such  people  should  have  is  not  very  readily 
accessible.  It  is  contained  in  various  articles  and  reports,  of  the 
existence  of  which  a  person  needing  information  would  probably 
be  ignorant.  Tims,  the  proceedings  of  the  sixteenth  annual  con- 
vention of  the  Master  Car-Builders'  Association  contains  a  report* 
of  a  special  committee  on  this  subject  which  gives  a  history  of 
what  has  been  done  in  relation  to  a  standard  system  of  screw- 
threads.  The  report,  however,  is  a  long  one,  and  probably  those 
who  want  to  learn  only  the  essential  principles  and  practice 
which  should  control  the  construction  of  standard  screw-threads 
would  not  have  the  time  or  patience  to  read  it.  One  of  the  diffi- 
culties in  the  way  of  the  general  introduction  of  the  standard 
system  of  screw-threads  is  that  there  are  so  many  persons  belong- 
ing to  the  class  described  who  do  not  know  what  the  standard  is 
which  has  been  recommended  for  general  adoption.  It  is  pro- 
posed in  this  article  to  describe  its  essential  features  in  as  simple 
and  clear  a  way  as  possible.  There  will  be  nothing,  or  very 
little,  that  will  be  new  in  what  is  said,  and  which  may  not  be 
found  in  other  publications.  All  that  is  aimed  at,  is  to  present 
the  essential  points  of  what  has  heretofore  been  stated,  in  as  clear 
and  simple  a  way  as  possible. 

It  will  not  be  necessary  to  say  to  the  persons  for  whom  we  are 
writing,  that  in  order  that  bolts  and  nuts  may  be  interchange- 
able, it  is  essential  that  they  should  have  the  same  number  of 

•Seepage  59,  Ante. 


84 

threads  to  the  inch,  as  obviously  a  f  nut  with  nine  threads  to  an 
inch  will  not  screw  on  a  bolt  with  twelve  without  injuring  or 
destroying  the  threads  of  one  or  both.  Therefore,  in  order  to 
make  bolts  and  nuts  interchangeable,  the  first  thing  which  had 
to  be  done  was  to  adopt  a  standard  number  of  threads  to  an  inch 
for  each  diameter  of  screws. 

Before  giving  the  number  of  threads  per  inch  which  is  now 
the  standard  in  this  country,  it  should  be  explained  that  "  in 
1864  the  inconvenience  and  confusion  resulting  from  the  diversity 
in  the  screw-threads  used  in  a  machine  and  other  construction  was 
brought  up  for  consideration  before  the  Franklin  Institute  of 
Philadelphia.  A  committee  was  then  appointed  to  investigate 
and  report  on  the  subject.  That  committee  recommended  the 
system  designed  by  Mr.  William  Sellers,  and  the  Institute  after- 
wards adopted  their  recommendation."  * 

In  1868  the  system  was  authorized  for  the  naval  service  by  the 
Secretary  of  the  Navy,  and  soon  after  the  Master  Mechanics' 
Association,  and  in  1871  the  Master  Car-Builders'  Association 
recommended  it  for  use  in  the  construction  of  locomotives  and 
cars. 

The  following  are  the  numbers  of  threads  to  an  inch  which  are 
specified  for  the  different  sizes  of  screws : 


Diameter  of  screw. 
%  inch,  . 
A 


y* 


No.  of  threads  per  inch. 
20 
18 
16 

.  14 

13 
12 
11 
10 

9 

8 

7 

7 


Unfortunately,  when  the  two  associations  named  recommended 
the  Sellers  system  of  screw-threads  for  use  on  railroads,  the  mem- 
bers did  not  seem  to  understand  fully  what  the  system  was,  and 
the  impression  was  very  general  among  the  members  that  it  con- 
sisted merely  of  the  specified  number  of  threads  to  an  inch.  The 


*  Page  78,  Reprinted  Report. 


85 

consequence  was  that  the  forms  of  the  threads  of  screws  made  at 
different  places  varied,  and  consequently  the  bolts  and  nuts  were 
often  not  interchangeable.  It  was  also  found  that  it  was  a  com- 
mon practice  among  iron  manufacturers  to  roll  iron  over-size, 
that  is,  iron  that  was  nominally  f  in.  in  diameter  was  found  to 
be  ^  or  ^  larger.  If  the  taps  and  dies  used  in  cutting  the 
screws  for  such  iron  were  of  the  exact  size,  it  of  course  was  nec- 
essary to  cut  away  the  excess  of  material,  which  injured  the  dies 
and  took  more  time.  To  avoid  this  it  was  a  very  common  prac- 
tice to  have  taps  and  dies  made  over-size ;  that  is,  £  taps,  instead 
of  being  of  that  diameter,  were  made  ^  or  ^V?  <>r  possibly  TV  in. 
larger  in  diameter  than  that  size.  This  of  course  made  it  impos- 
sible to  interchange  bolts  and  nuts  which  were  of  the  right  size 
with  those  which  were  larger,  and  as  there  was  no  common  prac- 
tice in  the  matter  of  over-size,  those  who  made  taps  and  dies  fa 
large  could  not  interchange  with  those  who  increased  the  size  TV 

It  was  also  found  that  even  where  different  manufacturers 
aimed  to  make  taps  and  dies  of  the  same  nominal  diameters,  they 
varied  from  these  sizes,  from  the  fact  that  they  had  no  common 
standards  of  measurement  of  sufficient  precision  to  insure  inter- 
changeability.  Investigation  showed,  too,  that  a  very  high  degree 
of  precision  is  required  in  the  manufacture  of  taps  and  dies,  in 
order  to  make  bolts  and  nuts  interchangeable,  and  that  a  differ- 
ence of  0.002  of  an  inch  in  the  diameter  of  a  |-in.  bolt  and  nut 
will  make  them  fit  each  other  loosely.  The  attention  of  those 
interested  in  the  matter  was  therefore  directed  to  the  means  of 
attaining  the  required  degree  of  precision.  The  efforts  of  those 
who  took  the  matter  up  were  seconded  by  The  Pratt  &  Whitney 
Company  of  Hartford,  Conn.,  which  Company  devoted  much 
time  and  money  to  investigating  the  subject,  and  to  perfecting 
the  machinery  required  to  make  gauges  of  the  required  accuracy 
to  insure  interchangeability.  As  it  would  take  too  much  space 
to  recount  the  successive  steps  which  it  was  necessary  to  take  to 
accomplish  the  end  aimed  at,  the  results  only  will  be  described 
here.* 

Before  doing  so,  it  should  be  fully  explained  that  the  Sellers 
system  of  screw-threads  consists  not  alone  in  the  number  of 
threads  to  an  inch,  but  the  diameters  of  the  screws  and  the  form 

I        *  See  Report  of  Committee,  page  59,  ante. 


86 

of  the  threads  are  also  distinctly  and  exactly  specified.  The 
angle  between  the  sides  of  the  thread  is  60°,  and  the  point  of  the 
thread  and  the  space  between  it  is  .flattened.  The  amount  taken 
off  the  point  and  that  filled  in  at  the  root  are  equal  to  one-eighth 
of  the  pitch.  Now  it  should  be  observed  that  all  these  dimensions 
and  proportions  are  definitely  specified.  For  example,  the  out- 
side diameters  of  Sellers  screws  are  •£,  TV  J,  T7ff,  &,  ^,  f,  f,  J,  1, 
li,  1J  in.  and  upward.  There  are  no  sizes  between  those  given. 
There  is  no  such  thing  as  a  screw  ff1¥  or  ^  in.  larger  or  smaller 
than  the  sizes  given  in  the  Sellers  system.  If  mechanics  wish  to 
adopt  the  Sellers  Standard,  they  must  therefore  adopt  these  sizes 
and  no  others. 

In  making  taps  and  dies  to  conform  to  the  Sellers  standard,  it 
is  therefore  important  that  the  diameter,  outside  and  at  the  root 
of  the  thread,  should  be  determined  with  sufficient  precision  to 
insure  interchangeability.  For  this,  and  other  similar  purposes, 
what  are  called  cylindrical  size-gauges,  figs.  7  and  8,  are  provided. 
The  first  is  a  hardened  steel  cylindrical  plug,  ground  and  lapped 


FIG.  7.  FIG.  8. 

perfectly  round  and  straight,  and  warranted  not  to  vary  more 
than  sTJviinr  of  an  inch  from  the  true  size.  Fig.  8  is  a  ring  which 
fits  the  cylindrical  plug.  Suitable  caliper  gauges,  for  use  in  the 
shop,  are  made  and  maintained  to  the  correct  size  from  the  cyl- 
indrical gauges.  In  the  manufacture  of  taps,  cylindrical  gauges 
are  made  for  their  outside  diameters,  and  also  for  the  diameters 
at  the  root  of  the  threads.  In  this  way  the  required  amount  of 
precision  in  these  dimensions  can  be  maintained. 

It  will  be  impossible  to  explain,  in  an  article  like  this,  the 
ingenious  methods  which  have  been  devised  for  making  chasing 
tools  which  will  cut  threads  whose  sides  will  have  an  inclination 
of  exactly  60°  to  each  other,  and  which  will  leave  just  the  right 
amount  of  material  at  the  root  of  the  threads.  All  this  work 
must  be  done  with  the  utmost  precision  to  insure  the  interchange- 
ability  of  bolts  and  nuts. 


87 

The  question  then  naturally  arises,  whether  this  degree  of  pre- 
cision can  be  maintained  if  the  work  of  manufacturing  taps  and 
dies  is  done  in  ordinary  shops.  Any  one  acquainted  with  the 
processes  and  appliances  needed  to  maintain  the  required  degree 
of  precision  must,  it  is  thought,  inevitably  conclude  that  if  inter- 
changeability  of  bolts  and  nuts  is  ever  brought  about,  it  will  be 
through  the  manufacture  of  taps  and  dies  b}7  firms  who  make  a 
specialty  of  the  business,  and  in  shops  supplied  with  all  the 
appliances  required  to  maintain  a  very  high  degree  of  precision. 

The  objection  to  having  them  made  by  one  firm  or  company  is 
that  it  would  inevitably  result  in  the  creation  of  a  monopoly, 
and  deprive  the  users  of  taps  and  dies  of  the  wholesome  influ- 
ence of  competition.  Therefore,  when  the  question  of  abandon- 
ing the  manufacture  of  these  tools  is  proposed  to  either  private 
firms  or  railroad  companies,  they  are  apt  to  object  to  placing 
themselves  in  a  position  in  which  they  would  not  have  the  privi- 
lege of  buying  such  tools  in  the  open  market.  What  they 
require  is  some  means  of  learning  whether  a  given  lot  of  taps 
and  dies  conform  near  enough  to  the  standard  dimensions  and 
proportions  to  insure  the  interchangeability  of  the  bolts  and  nuts 
made  with  them.  To  meet  this  requirement,  The  Pratt  & 
Whitney  Company  make  what  is  called  "  internal  and  exter- 
nal standard  thread  gauges,"  represented  by  figs.  9  and  10. 


FIG.  9.  FIG.  10. 

The  internal  gauge  (fig.  9)  consists  of  a  threaded  cylinder,  made 
to  exact  standard  size,  and  the  external  gauge  has  a  corresponding 
screw-thread,  which  is  adjustable  to  the  internal  gauge.  With  a 
set  of  these  gauges,  the  nuts  and  bolts  cut  by  any  taps  or  dies  can 
be  tested  at  once,  and  it  can  be  known  whether  they  conform  to 
the  standard  sizes.  With  such  a  set  of  gauges  in  the  tool-room  of 
a  railroad  or  other  shop,  the  person  in  charge  can  at  once  know 
whether  taps  and  dies  bought  of  any  firm  are  of  the  right  size. 
This  leaves  the  purchaser  free  to  buy  in  the  open  market,  and  at 
the  same  time  maintains  the  standard  at  the  required  degree  of 
precision. 


88 

In  adopting  the  Sellers,  or  Franklin  Institute,  or  United  States 
standard,  as  it  is  variously  called,  a  difficulty  arose  from  the  fact 
that  it  is  the  habit  of  iron  manufacturers  to  make  iron  over-size, 
and  as  there  are  no  over-size  screws  in  the  Sellers  system,  if  iron 
is  too  large  it  is  necessary  to  cut  it  away  with  the  dies.  So  great 
is  this  difficulty,  that,  as  already  explained,  the  practice  of  mak- 
ing taps  and  dies  over-size  has  become  very  general.  If  the 
Sellers  system  is  adopted,  it  is  essential  that  iron  should  be 
obtained  of  the  correct  size,  or  very  nearly  so.  Of  course  no 
high  degree  of  precision  is  possible  in  rolling  iron,  and  when 
exact  sizes  were  demanded,  the  question  arose  how  much  allowa- 
ble variation  there  should  be  from  the  true  size.  The  matter 
was  discussed  at  a  meeting  of  the  Master  Car-Builders'  Club 
during  the  past  winter  (Dec.  21,  1882),  and  after  consultation 
with  different  iron-makers  it  was  concluded  that  there  might  be  a 
variation  of  about  0.01  in.  in  the  smallest  sizes,  0.015  in.  in  J--in. 
and  0.02  in  1  in.  iron.  It  was  suggested,  too,  that  limit  gauges 
should  be  made  for  inspecting  iron.  It  was  proposed  to  make 
these  of  caliper  form,  with  two  openings,  one  larger  and  the 
other  smaller  than  the  standard  size,  and  then  specify  that  the 
iron  should  enter  the  large  end  and  not  enter  the  small  one. 
After  further  discussion  it  was  agreed  to  make  the  difference  in 
the  size  of  the  large  and  the  small  end  of  the  gauge  for  £-in. 
iron  0.01  in.,  and  increase  the  difference  by  0.001  in.  for  the  sizes 
above  that.  The  following  table  of  dimensions  for  the  limit 
gauges  was  therefore  drawn  up,  and  was  recommended  by  the 
Master  Car-Builders'  Association : 


Size  of  iron. 

Size  of  large 
end  of  gauge. 

Size  of  small 
end  of  gauge. 

Difference  in 
size  of  large 
and  of  small 
end  of  iron. 

£  

0  2550 

0  2450 

0010 

JL 

0  8180 

0  3070 

0  Oil 

4  • 

0  3810 

0  3690 

0  012 

?  

0  4440 

04310 

0013 

*  . 

0  5070 

0  4930 

0  014 

A  • 

0  5700 

0  5550 

0  015 

p..                  '"::  : 

0  6330 

06170 

0  016 

i  .  .  .  . 

0  7585 

0  7415 

0  017 

^  

08840 

08660 

0  018 

i  

1  0095 

0.9905 

0.019 

1  1350 

1  1150 

0020 

H. 

u  • 

1  2G05 

1  2395 

0.021 

The  Pratt  &  Whitney  Company  took  the  matter  up,  and  at 
the  Chicago  Exposition  of  Railway  Appliances  exhibited  a  com- 
plete set  of  such  gauges,  one  of  which  is  represented  by  Fig.  11 . 


FIG.  11. 

It  is  obvious,  though,  that  if  used  in  inspecting  iron,  such 
gauges  would  soon  wear  so  as  not  to  be  sufficiently  accurate  for 
the  purpose  for  which  they  are  intended.  To  provide  for  this 
the  company  has  also  made  "  standard  reference  gauges,"  Fig.  12, 


FIG.  12. 

consisting  of  a  series  of  cylindrical  gauges,  arranged  like  steps, 
those  at  one  end  being  of  the  sizes  of  the  small  end  of  the  cali- 
per-gauges,  and  those  at  the  other  end  the  sizes  of  the  large  end. 
Whenever  it  is  suspected  that  the  caliper-gauges  have  been  injuri- 
ousty  worn,  they  can  be  tested  with  the  reference  gauge  and  the 
required  correction  made.  In  this  way  their  accuracy  can  be 
maintained. 

The  question  is  often  asked  by  master  mechanics,  car-builders, 
and  others,  "What  must  we  do  to  adopt  the  Sellers,  Franklin 
Institute,  or  United  States  standard  system  of  screw-threads?" 
From  what  has  been  said  it  will  be  seen  that,  in  taking  these 
steps,  what  is  required  is : 

1.     Abandon  the  manufacture  of  taps  and  dies  altogether. 


90 

2.  Get  a  set  of  screw-gauges  for  testing  the  accuracy  of  the 
taps  and  dies  that  are  bought. 

3.  Get  a  set  of  limit  gauges  for  round  iron,  and  require  man- 
ufacturers to  make  iron  to  the  size  of  those  gauges,  and  then 
have  every  lot  received  inspected. 

4.  Abandon    entirely   the  use   of  over-size  screws   for   new 
work. 


STANDARD  LIMIT  GAUGES  FOR  EOUND  IRON. 

In  accordance  with  a  resolution  of  the  Master  Car-Builders' 
Association  and  its  constitution,  a  circular  was  mailed  last 
November  *  by  Mr.  M.  BT.  Forney,  the  Secretary,  to  the  several 
members,  containing  the  following  : 

"  In  introducing  the  Sellers  or  Franklin  Institute  standard  sys- 
tem of  screw-threads  a  serious  difficulty  has  been  encountered, 
owing  to  the  fact  that  round-bar  iron  has  heretofore  been  very 
generally  rolled  over-size  —  that  is,  it  has  been  made  a  small 
fraction  of  an  inch  larger,  and  in  some  cases  smaller,  than  its 
nominal  diameter.  In  order  to  have  standard  screws  of  the  cor- 
rect diameter  it  is  therefore  necessary  to  cut  down  the  iron  with 
the  screw-cutting  dies,  which  causes  them  to  wear  rapidly ;  and, 
inasmuch  as  the  screw,  if  it  is  of  the  same  or  less  diameter  than 
the  bolt,  is  the  weakest  part,  there  is  a  great  waste  of  material 
when  the  bolt  is  of  larger  diameter  than  the  screw.  It  is  there- 
fore desirable  that  round  iron  should  be  made  of  the  right  size, 
so  that,  in  cutting  standard  screws,  there  will  be  as  little  waste 
as  possible.  But,  as  it  is  impracticable  to  roll  iron  to  exact  sizes, 
some  variation  in  diameter  must  be  allowed.  Therefore,  in 
specifying  the  size,  all  that  can  be  required  is  that  the  iron  shall 
not  be  larger  than  a  certain  dimension,  nor  smaller  than  another. 

"To  make  it  easy  to  determine  whether  the  size  of  iron  is 
within  given  limitations,  it  has  been  proposed  to  use  a  limit 
gauge,  like  that  represented  by  fig.  11,  consisting  of  double  fixed 
calipers,  one  end  of  which  is  a  fraction  of  an  inch  larger  than 
the  standard  size,  and  the  other  a  fraction  of  an  inch  smaller, 

*  See  Report  of  the  Proceedings  of  the  17th  Annual  Convention  of  the  Master  Car-Builders' 
Association,  held  in  Chicago,  Jane,  1883. 


91 


and  then  require  that  all  iron  of  the  nominal  size  of  the  gauge 
shall  be  so  large  as  not  to  enter  its  small  end,  and  so  small  that  it 
will  enter  the  large  end.  Before  such  limit  gauges  could  be 
made  or  their  use  adopted,  it  was  essential  to  establish  a  standard 
for  the  difference  in  size  of  the  large  or  -f  end  and  the  small  or 
—  one.  With  this  end  in  view  the  following  resolution  was  pre- 
sented at  the  last  annual  Convention  of  the  Master  Car-Builders' 
Association  : 

"Resolved,  That  the  following  sizes  for  limit  gauges  for  round  iron  for  the 
Sellers  standard  threads  are  hereby  established  by  the  Master  Car-Builders' 
Association  as  the  standard  sizes  for  such  gauges,  and  it  is  recommended  that 
round  iron  of  the  nominal  standard  sizes  be  made  of  such  diameter  that  each  one 
will  enter  the  larger  or  +  end  of  the  gauge  intended  for  it,  in  any  way,  and 
will  not  enter  the  small  or  —  end  in  any  way" 


Diameter. 
Inches. 

Large  size, 
-fend. 
Inches. 

Small  size, 
—  end. 
Inches. 

Total 
variation. 
Inches. 

i 

2550 

2450 

010 

A   . 

3180 

3070 

Oil 

4  . 

3810 

3690 

012 

.4440 

4310 

013 

-i 

5070 

4930 

014 

A 

5700 

5550 

015 

1.  . 

6330 

6170 

016 

1  . 

7585 

7415 

017 

'    I 

8840 

8660 

018 

\ 

1  0095 

0  9905 

019 

11.  . 

1  1350 

1  1150 

020 

li.  . 

1  2605 

1  2395 

021 

In  accordance  with  the  constitution,  blank  ballots  were  sent 
out  to  the  members  by  the  Secretary,  asking  a  vote  on  the  adop- 
tion of  the  above  resolution.  Sixty  days  after  sending  these 
ballots,  as  the  constitution  requires,  the  ballots  received  were 
counted,  and  the  Secretary  announces  that  81  ballots  were  cast, 
aggregating  301  votes,  of  which  291  were  in  favor  of  the  resolu- 
tion. More  than  two-thirds  having  voted  for  the  standard,  it  was 
adopted." 


92 


[Reprinted  from  the  Journal  of  the  Franklin  Institute,  April,  1887 

THE   SELLERS   OR  FRAJSTKLIN  INSTITUTE  SYSTEM 
OF  SCREW-THREADS. 

The  following  correspondence  has  grown  out  of  an  inquiry 
addressed  to  the  INSTITUTE  by  the  Society  of  German  Engineers 
of  Berlin,  and  is  self-explanatory.  W.  H.  W. 

BERLIN  W.,  den  22.  October,  1886, 

Wichmannstrassee  14. 

An  das  FRANKLIN   INSTITUTE,  Philadelphia  (V.  St.  A.)  15  Smith 
Seventh  Street. 

Fur  die  in  unserm  Yereine  noch  immer  im  Gange  befindliche 
Agitation  zur  Aufstellung  eines  einheitlichen  Schraubengewinde- 
systems  auf  Grundlage  des  Metermaasses  wfirde  es  uns  von  hohem 
Werthe  sein,  die  Yerhandlungen  und  Beschlusse  eines  verehrlichen 
FRANKLIN  INSTITUTE  fiber  diese  Frage  kennen  zu  lernen ;  insbe- 
sondere  wurde  es  uns  interessiren,  zu  erfahren,  ob  in  den  Yer. 
Staaten  ein  Standard -Gewinde  aufgestellt  ist,  und  zwar  welches, 
und  welche  Geltung  es  bisher  erlangt  hat. 

In  der  Zeitschrift  Engineering,  vom  10.  September  d.  J.,  ist  ein 
Aufsatz,  welcher  unter  Anderem  die  Behauptung  enthalt,  dass  das 
von  Sellers  vorgeschlagene  Gewinde,  mit  geraden  Flachen  statt  der 
Whitworth'schen  Abrundungen,  als  nicht  bewahrt  befunden  und 
wieder  aufgegeben  worden  sei ;  auch  hieruber  waren  uns  Mitthei- 
lungen  sehr  erwfinscht. 

Mit  Freuden  bereit,  auch  Ihnen  vorkommenden  Falles  zu 
Diensten  zu  sein,  zeichnen  wir 

Hochachtungsvoll, 

DER  YEREIN  DEUTSCHER  INGENIEURE. 
Th.  Peters. 

[Translation. ~\ 

BERLIN  W.,  October  22,  1886. 
To   the   FRANKLIN   INSTITUTE,    Philadelphia  (U.  S.  A.)  15  South 

Seventh  Street. 

In  connection  with  the  subject  of  establishing  a  uniform  system 
of  screw-threads  based  on  the  metrical  system  —  which  for  a  long 


93 

time  lias  been  agitated  by  this  society —  it  would  be  of  the  greatest 
value  to  us  to  be  advised  respecting  any  proceedings  taken  and 
conclusions  reached  by  the  FKANKLIN  INSTITUTE  upon  this  subject. 
It  would  especially  interest  us  to  learn  if  any  standard  has  been 
adopted  in  the  United  States,  and  if  so,  what  standard,  and  to 
what  extent  it  has,  up  to  the  present  time,  received  acceptance. 

In  Engineering,  of  September  10, 1886,  there  appears  an  article 
on  this  subject,  in  which  the  assertion  is  made,  that  the  system  of 
threads,  proposed  by  Sellers  —  having  straight  surfaces  instead  of 
the  rounded  ones  of  Whitworth  —  had  not  been  found  to  fully  meet 
the  requirements  of  practice,  and  had  been  abandoned.  On  this 
point,  also,  any  information  would  be  very  acceptable.  With  the 
expression  of  our  willingness  to  serve  you,  should  the  occasion 
offer  itself,  we  subscribe  ourselves, 

With  high  regard, 

THE  SOCIETY  OF  GERMAN  ENGINEERS. 
Th.  Peters. 


The  article  in  (London)  Engineering,  herein  referred  to,  is  given 
below,  viz. : 

In  the  year  1857,  many  of  the  leading  engineers  in  England  began 
to  recognize  the  evil  and  the  very  great  inconvenience  which  arose 
from  various  quarters  through  individual  machine  and  engine  makers 
using  a  separate  system  of  screw-threads.  So  important  did  Sir 
Joseph  Whitworth  consider  the  matter,  that  he  undertook  to  establish 
and  introduce  a  uniform  system  of  standard  pitches  and  form  of  thread 
for  use  throughout  the  country.  His  first  table  was  published  in  the 
same  year,  viz.,  1857,  and  a  second  one  in  1861,  in  which  he  gave 
fuller  particulars,  and  proposed  a  few  minor  improvements.  The  main 
points  to  be  considered  in  arranging  such  a  system  were,  briefly  : 

(I.)  The  best  and  most  suitable  pitches  or  number  of  threads  per 
inch  of  length  for  given  diameters  of  bolts,  the  main  object  being  to 
reduce  the  strength  of  the  bolt  as  little  as  possible,  and  at  the  same 
time  to  make  the  threads  of  sufficient  depth  to  prevent  liability  to 
"  cross-threading  "  taking  place,  and  to  get  a  convenient  thickness  of 
nut  which  would  stand  at  least  as  much  longitudinal  tensile  stress  as 
the  bolt  at  the  bottom  of  the  thread.  After  very  careful  consideration 
on  the  part  of  Sir  Joseph  Whitworth,  he  decided  upon  a  set  of  pitches 


94 

which  were  published  in  tabular  form,  copies  of  which  are  found  in 
all  engineering  text-books.  The  following  formula,  taken  from 
Un win's  Machine  Design,  page  117,  gives  a  very  close  approximation: 

Let  d  =  the  original  diameter  of  the  bolt. 
p  =  the  pitch  of  the  threads. 

Then 

p  =  0.08  d+  004, 

and  the  diameter  at  the  bottom  of  the  thread, 
d'—  0.9  d  —  0.05. 

(2.)  The  form  or  cross-section  of  the  thread  best  suited  for  practi- 
cal purposes,  which  involved  the  consideration  of  ease  of  manufacture 
and  reproduction,  combined  with  security  against  damage  by  the  com- 
paratively rough  treatment  bolts  and  screws  are  subjected  to.  The 
form  of  cross-section  Whitworth  adopted  for  ordinary  purposes  was 
that  of  a  triangle,  whose  height  was  0.96  pitch  and  the  angle  at  the 
bottom  of  the  threads  55°  (see  Unwin's  Machine  Dexign,  page  117); 
one-sixth  of  these  triangular  sections  was  rounded  off  at  the  top  and 
bottom.*  This  system  has  been  very  widely  and  almost  universally 
used  for  the  last  thirty  years,  the  chief  and  only  important  exception 
to  their  universality  being  in  the  United  States,  where  Sellers's  threads 
are  very  much  used;  they  are  of  a  slightly  different  pitch  and  form  of 
cross-section,  being  an  equilateral  triangle  with  one-eighth  of  the 
depth  cut  off  square,  both  top  and  bottom;  the  pitch  is  nearly 
p  =  0.1  d  -f  0.025,  and  the  diameter  at  the  bottom  of  thread 
dl  =  0.87  d — 0.03.  (See  Unwin's  Machine  Design,  page  119.) 

The  relative  values  of  these  two  systems  lie  chiefly  in  the  merits  of 
round  or  sharp  corners.  We  shall  return  presently  to  consider  both 
systems  in  detail,  but  it  is  well  to  note  here  that  the  latter  system  is 
being  discarded  for  one  very  similar  to  the  Whitworth.  This  is  briefly 
how  the  screw-thread  question  stands  at  the  present  time.  However, 
in  Germany  and  on  the  continent  of  Europe  generally,  the  English 
system  of  measurement  in  feet  and  inches  is  not  in  common  use,  but 
the  metrical  system  is  almost  universal,  viz.,  of  meters  with  decimal 
subdivisions.  Hence,  a  small  body  of  German  engineers  have  been 
for  some  time  urging  for  a  universal  metrical  standard  of  screw-threads, 
and  consequently  seek  to  overthrow  the  Whitworth  system. 

In  1874,f  the  Miinchen  District  Society  of  German  Engineers  took 
up  the  matter,  when  they  not  only  procured  the  opinions  of  the  Ger- 
man district  societies,  but  communicated  with  various  well-known  Con- 

*  See  page  60,  Ante. 

t  Vide  a  paper  "  On  the  Thread  Question,1'  by  J.  H.  Mehrtons,  engineer,  of  Berlin. 


95 

tmental  engineering  societies,  and  at  the  same  time  sent  out  2,000  cir- 
culars to  owners  of  works  to  obtain  their  views  upon  the  practicability 
of  introducing  a  metrical  system  in  the  place  of  Whitworth's,  maintain- 
ing that  this  system  was  not  in  general  use;  but  the  result  of  this 
inquiry  was  in  favor  of  retaining  the  Whitwortb  system. 

Out  of  the  2,000  circulars  sent  out,  only  365  were  returned,  316  of 
which  were  from  makers  who  used  the  Whitworth  system  exclusively, 
and  the  remaining  forty-nine  retained  the  pitch,  but  used  different 
diameters  of  bolts.  Of  the  twenty  district  societies  which  were  con- 
sulted, only  six  decided  in  favor  of  the  metrical  system.  The  practi- 
cal effect  of  this  inquiry  was  to  set  the  Whitworth  system  on  a  firmer 
basis  than  ever.  In  spite  of  this,  however,  the  Karlsruhe  District 
Society  brought  forward  motions  in  favor  of  the  metrical  system  at 
the  principal  meeting  of  the  Society  of  German  Engineers  in  1877, 
but  they  were  at  once  dismissed  by  them.  Again,  in  1885,  the  same 
society  brought  up  the  matter  under  a  rather  different  aspect,  viz.,  not 
whether  it  was  desirous  to  introduce  a  metrical  system  of  screw-threads, 
but  what  metrical  system  shall  be  introduced,  implying  that  the  former 
was  a  settled  matter,  and  the  only  matter  requiring  consideration  was 
the  details  of  the  system. 

The  directorate  thought  it  desirable  to  appoint  a  special  commission 
to  inquire  into  it.  The  main  objections  brought  against  the  Whit- 
worth system  by  the  commission  and  the  Karlsruhe  Society,  were 
briefly: 

(1.)  The  Whitworth  system  is  not  universally  used  in  Germany, 
and  consequently  great  disorder  prevails. 

(2.)  The  Whitworth  system  being  measured  in  inches,  it  is  incon- 
venient for  metrical  measurements. 

(3.)  The  cross-section  of  the  Whitworth  thread  is  difficult  of  manu- 
facture. 

The  first  objection  has  been  dealt  with  above  in  the  remarks  on  the 
action  taken  by  the  Karlsruhe  and  Miinchen  District  Societies,  and, 
again,  the  Whitworth  system  is  universally  used  by  the  German  rail- 
ways and  dockyards,  and  unless  a  general  desire  is  shown  for  a  metri- 
cal system  of  threads,  it  is  evidently  quite  useless  for  a  handful  of 
o-bscure  scientific  men  to  attempt  a  radical  change  in  such  an  import- 
ant matter. 

The  second  objection,  on  the  surface,  appears  slightly  more  justifia- 
ble, but  even  that  is  extremely  insignificant  when  more  closely  exam- 
ined and  viewed  from  a  different  standpoint.  This  matter  does  not 
stand  upon  the  same  ground  that  it  did  ten  years  ago,  when  the  whole 


96 

of  the  bolts  and  screws  in  use  were  constructed  in  small  quantities  as 
they  were  required  at  the  various  machine  and  engine  works;  to-day 
the  case  is  totally  different,  as  only  a  very  small  percentage  are  con- 
structed  in  this  way ;  they  are  almost  entirely  bought  from  special 
screw-makers,  who  turn  out  better  and  cheaper  work  than  is  possible 
fcr  individual  machine  shops.  Thus  the  imaginary  difficulty  lies 
entirely  in  the  screw-makers'  hands.  They  do  not  complain;  why, 
then,  should  those  whom  it  does  not  affect  to  any  appreciable  extent  ? 

If  a  new  universal  system  of  screw-threads  must  be  adopted,  then  it 
should  not  be  tied  down  to  any  special  system  of  measurement,  but 
should  rather  be  designed  on  a  system  of  standard  gauges  of  various 
grades,  similar  to  our  Birmingham  wire-gauge  system.  Some  of  the 
German  engineers  complain  that  a  considerable  number  of  Whitworth 
bolts  and  nuts  purchased  from  one  firm  of  screw  makeis,  will  not  fit 
those  purchased  from  another  firm,  and  lay  the  blame  to  the  system  ; 
but  this  is  decidedly  unjust,  for  it  is  evident  to  any  practical  engineer 
that  the  fault  lies  not  in  the  system  itself,  but  with  the  manufacturers 
for  not  using  standard  screw-gauges,  as  Sir  Joseph  Whitworth  advo- 
cated in  his  original  report  on  the  subject.  None  can  say  but  what 
the  proposed  new  system  would  be  quite  as  faulty,  perhaps  even  worse 
in  this  respect,  as  it  has  never  been  practically  put  to  the  test.  If 
German  engineers  persist  in  their  course,  and  carry  out  this  proposed 
scheme  in  the  machinery  they  manufacture,  they  only  will  be  the  suf- 
ferers by  ruining  their  foreign  trade,  for  no  foreigners  will  think  of 
purchasing  machinery  which  cannot  readily  be  repaired  by  local  engi- 
neers  without  sending  to  Germany  for  special  bolts  and  nuts. 

The  third  objection  is  totally  unjustifiable,  for  thirty  years  of  prac 
tice  have  most  unmistakably  proved  the  Whitworth  form  of  cross-sec- 
tion to  be  the  best.  The  square-tipped  thread,  on  the  other  hand,  as 
advocated  by  the  metrical  system,  has  proved  unsuccessful.  It  has 
been  thoroughly  tried  by  Sellers  in  the  United  States,  where  it  has 
been  found  practically  impossible  to  produce  a  good  thread  by  screw- 
ing apparatus;  the  sharp  corners  on  the  taps  and  dies  rapidly  break 
away,  when  a  very  imperfect  thread  must  naturally  follow.  The 
present  state  of  affairs  in  America  conclusively  shows  the  system  to 
have  been  a  failure,  and  all  the  leading  machine  tool-makers  there  are 
supplying  nothing  but  the  V-thread,  very  similar  to  Whitworth's. 

Again,  the  strength  of  the  bolt  is  reduced  more  by  the  square-cor- 
nered than  by  the  rounded  thread,  although  the  sectional  areas  of  the 
bolts  at  the  bottom  of  the  threads  are  the  same;  for  example,  it  is 
always  found  to  be  absolutely  necessary  in  the  preparation  of  test 


97 

specimens  for  tensile  tests  to  have  the  corners  well  rounded  oft';  if 
not.  the  specimen  almost  invariably  breaks  short  off  at  the  square 
corner.  With  good  tools  and  good  men  to  use  them,  there  is  no  diffi- 
culty whatever  in  producing  the  Whitworth  cross  section  of  thread. 
The  round  at  the  bottom  of  the  thread  is  easily  pi  oduced  by  a  rounded 
point  to  the  screw-cutting  tool,  a  gauge  for  which  is  carried  by  every, 
turner  in  his  waistcoat  pocket.  The  round  at  the  top  of  the  thread  is 
produced  by  the  chaser,  which  is  itself  cut  by  a  standard  hob,  and 
consequently  reproduces  the  correct  form  of  cross-section  on  whatever 
work  it  is  used. —  Engineering,  Sept.  10,  1886. 

SECRETARY'S  OFFICE,  HALL  OF  THE  FRANKLIN  INSTITUTE, 

PHILADELPHIA,  Jan.  31,  188T. 
The  Society  of  German  Engineers: 

GENTLEMEN:  —  In  response  to  your  letter  of  October  22d  ult., 
asking  to  be  informed  respecting  any  proceedings  taken  and  con- 
clusions reached  by  this  INSTITUTE  upon  the  subject  of  establish- 
ing a  uniform  system  of  screw-threads,  whether  any  standard  has 
been  adopted  in  the  United  States,  and  if  so,  what  standard,  and 
to  what  extent  it  has,  up  to  the  present  time,  received  accept- 
ance, also  referring  to  an  article  in  Engineering  of  September  10,. 
1886,  with  quotation  therefrom,  I  have  the  honor  to  report: 

The  proceedings  taken  by  the  FRANKLIN  INSTITUTE  with  refer- 
ence to  a  uniform  system  of  screw-threads  wTere  inaugurated  by. 
a  paper  upon  this  subject  by  Mr..  William  Sellers,  read  by  him, 
before  the  INSTITUTE  at  its  regular  monthly  meeting,  held  April, 
21, 1864  (see  copy  of  the  Journal  for  April  of  that  year,  forwarded,, 
with  other  papers  hereinafter  referred  to,  by  book-post,  on  tlm 
31st  inst.).  This  was  followed  by  the  appointment  of  a  commit- 
tee to  investigate  and  report.  The  report  of  this  committee  will, 
be  found  in  the  number  of  the  Journal  for  January,  1865,*  for- 
warded as  above,  and  this  ended  the  proceedings  so  far  as  the 
FRANKL.IN  INSTITUTE  was  concerned.  Early  in  1868,  the  Secre- 
tary of  the  Navy  of  the  United  States  appointed  a  board  of  engi- 
neers to  investigate  and  report  upon  a  system  of  screw-threads 
which  might  with  advantage  be  adopted  by  that  department  of 
the  government,  and  this  board  reported  May  9,  1868,  recom- 
mending the  system  advocated  by  Sellers  and  approved  by  this 

*  See  copy  of  this  report,  page  78. 
7 


98 

INSTITUTE  (see  copy  of  report  forwarded  as  above).  This  report 
was  approved  by  the  Secretary  of  the  Navy,  and  thenceforth  it 
has  been  the  standard  of  the  United  States  Government,  not  only 
for  the  Navy  Department,  but  for  all  other  departments,  except- 
ing for  small  arms  and  other  specific  requirements,  where  a  much 
finer  thread  is  necessitated.  This  action  by  the  government  was 
followed  by  its  general  adoption  in  the  large  private  establish- 
ments all  over  the  country  engaged  in  constructing  the  heavier 
classes  of  machinery. 

In  April,  1869,  the  Pennsylvania  Railroad  Company  ordered  a 
set  of  gauges  to  the  new  form  of  thread,  and  adopted  the  system 
upon  all  of  its  lines,  and  this  was  followed  by  various  other  rail- 
roads throughout  the  country,  until,  in  1872,  the  Master  Car 
Builders'  Association  recommended  the  Sellers  or  FRANKLIN  IN- 
STITUTE system  of  screw-threads  and  bolts  as  a  standard.  The 
progress  thereafter  in  this  direction  is  shown  by  the  Report  of  the 
Proceedings  for  1885,  forwarded  as  above,  and  similar  action  was 
taken  by  the  Master  Mechanics'  Association. 

To  answer  your  inquiry,  "  to  what  extent  it  has,  up  to  the 
present  time,  received  acceptance,"  and  also  the  "  article  in 
Engineering"  before  referred  to,  the  secretary  of  the  INSTITUTE 
addressed  the  following  letter  to  the  proper  officers  of  the  princi- 
pal railroads  in  the  United  States,  and  to  several  individual 
manufacturers : 

PHILADELPHIA,  December,  1886. 
To  the  Superintendent  of Railroad  Company: 

DEAR  SIR:  —  The  Society  of  German  Engineers  of  Berlin  has  made 
certain  inquiries  of  the  FRANKLIN  INSTITUTE  concerning  the  Standard 
Screw-Thread  recommended  for  general  adoption  by  the  FRANKLIN 
INSTITUTE  in  1864,  and  adopted  by  the  Navy  Department  of  the  United 
Stales  in  1868,  among  which  inquiries  the  durability  of  the  straight 
surfaces,  as  compared  with  the  rounded  ones  of  Whitworth,  is  ques- 
tioned. It  is  probable  that  the  straight  surfaces  of  the  standard  thread 
would  show  a  modification  of  form  to  the  eye  which  would  not  be 
observable  upon  the  curved  surface  of  the  Whitworth  thread  ;  but,  as 
some  contribution  to  this  inquiry,  it  would  be  of  interest  to  know 
whether  the  standard  thread  has  been  adopted  upon  your  road,  and 
whether  you  have  experienced  any  difficulty  in  practically  maintaining 
the  form  of  the  thread,  or  at  least  sufficiently  so  as  to  make  the  nuts 


99 

interchangeable.  If  you  find  that  the  straight  surfaces  are  more  diffi- 
cult to  maintain  than  the  curved  ones  of  the  Whitwortli  thread,  would 
this  be  counterbalanced  by  the  greater  facility  for  making  the  straight 
thread  with  a  single  tool  overthat  of  the  curved  thread,  which  requires 
two  (2)  tools,  and  which  form  of  thread  can  most  easily  be  constructed 
and  tested,  for  accurate  conformity  with  a  standard  of  its  form?  Any 
information  you  can  give  me  in  connection  with  this  subject  will  be 
highly  appreciated  by,  etc., 

Yours  truly,          WM.  H.  WAHL,  Secretary. 

In  response  to  this  letter,  lie  has  received  replies  from  the  fol- 
lowing railroad  companies : 

Pennsylvania  Railroad  Company,  operating  and  controlling 
7,346  miles  of  railroad. 

Chicago,  Milwaukee  &  St.  Paul  Railway  Co.,  4,921  miles. 

New  York  Central  &  Hudson  River  Railroad  Co.,  993  miles. 

Chicago,  Rock  Island  &  Pacific  Railroad  Co.,  1,383  miles. 

Delaware,  Lackawanna  &  Western  Railroad  Co.,  889  miles. 

Louisville  &  Nashville  Railroad  Co.,  3,727  miles. 

Chicago,  Burlington  &  Quincy  Railroad  Co.,  3,646  miles. 

New  York,  Lake  Erie  &  Western  Railway  Co.,  1,601  miles. 

He  has  also  a  reply  from  one  of  our  largest  manufacturers  of 
bolts  and  nuts,  and  one  from  our  most  important  manufacturers  of 
taps  and  dies.  The  article  in  the  Railroad  Gazette,  of  September 
24,  1886,  referred  to  by  the  latter  is  forwarded  by  book-post  with 
the  other  paper  hereinbefore  referred  to. 

THE  LETTERS  received  in  response  to  the  Secretary's  inquiry 
are  as  follows : 

Louisville  &  Nashville  Raikoad   Company,   Office  of  Superintendent 

Machinery. 

LOUISVILLE,  KY.,  December  6,  1886. 
WM.  H.  WAHL,  ESQ.,  Secretary  FEANKLIN  INSTITUTE,  Philadelphia,  Pa. 

DEAR  SIR:  —  Yours  of  December  14th  is  at  hand  and  noted.  We 
adopted  the  United  States  Standard  Thread,  sometimes  called  the 
FRANKLIN  INSTITUTE  Thread,  about  five  (5)  years  ago,  in  all  the  shops 
of  our  lines,  and  have  used  it  ever  since.  We  have  found  no  difficulty 
whatever  from  the  wearing  of  the  taps  and  dies  as  long  as  they  are 
not  used  beyond  a  proper  length  of  time.  Of  course,  as  taps  and  dies 
wear  away,  it  will  make  a  slight  difference  in  the  form  of  the  thread; 


100 

but  I  do  not  believe  that  that  change  is  any  greater  or  can  give  any 
more  trouble  than  in  the  case  of  the  Whit  worth  thread  referred  to. 
We  have  experienced  no  difficulty  in  the  interchange  of  nuts  and  bolts 
on  account  of  the  slight  change  that  occurs  in  the  form  of  the  thread 
in  the  wearing  of  the  taps  and  dies.  Of  course,  any  form  of  thread 
will  change  slightly  from  the  wearing  of  the  taps  and  dies,  and  it  is 
impossible  to  avoid  that  by  any  form  of  thread  uc-ed.  A  straight  side 
to  a  thread  is  easier  to  make  than  a  rounding  side,  and  therefore  more 
likely  to  be  perfect.  A  straight  side  to  a  thread,  it  seems  to  me,  will 
change  as  little,  perhaps  less,  than  a  rounding  side.  The  proper  way 
to  keep  threads  as  near  the  original  as  possible  is  to  throw  away  the 
taps  and  dies  before  they  are  worn  to  such  an  extent  as  will  make  any 
practical  difference  in  the  shape  of  the  thread.  This  is  a  matter  that 
is  sometimes  overlooked.  The  expense  of  taps  and  dies  is  not  great, 
and  only  perfect  taps  and  dies  should  be  used;  and  as  soon  as  the 
wear  amounts  to  enough  to  make  an  appreciable  difference  in  the  form 
of  the  thread,  they  should  be  thrown  away  and  renewed.  We  have 
made  it  a  rule  to  purchase  from  reliable  manufacturers  nearly  all  of 
our  taps  and  hobs  for  cutting  dies,  and  we  have  been  particular  to 
throw  away  taps  as  soon  as  they  are  worn  to  any  considerable  extent, 
and  use  new  ones.  The  same  in  regard  to  dies;  as  soon  as  to  amount 
to  anything,  we  re-cut  them,  dress  them  up,  and  then  they  are  as  good 
as  new.  It  seems  to  me  a  flat-top  form  of  thread  will  change  as  little 
as  a  thread  that  runs  to  a  point.  It  will  change  less  in  diameter  from 
out  to  out  of  the  thread.  With  a  sharp-top  thread,  when  the  sides 
wear  away  slightly,  it  reduces  the  height  of  the  thread.  With  a  flat- 
top thread  the  wear  of  the  sides  will  not  reduce  the  diameter  from  out 
to  out  of  the  thread,  but  will  simply  make  the  thread  a  little  thinner 
at  the  point,  etc.  Yours  truly, 

R.  WELLS,  Superintendent  Machinery. 


Delaware,  Lackawanna  &  Western  Railroad   Company^  Office  of  Machine 

Shops. 

SCRANTON,  PA  ,  December  8,  1886. 

MR,  WM.  H.  WAHL,  Secretary  FRANKLIN  INSTITUTE,  Philadelphia,  Pa. 
DEAR  SIR: — Replying  to  yours  of  the  4th  inst.,  in  regard  to  the 
Standard  Screw-Thread,  would  say,  the  United  States  Standard  has 
been  adopted  on  this  road  and  gives  entire  satisfaction.     It  is  much 
easier  to  make,  and  the  tools  to  make  it  less  expensive  to  keep  up, 
Yours  truly,  CHAS.  GRAHAM,  Master  Mechanic. 


101 

Chicago,    Milwaukee    &    St.    Paul    Railway,    Office    of    General    Master 

Mechanic. 

WEST  MILWAUKEE,  Wis.,  December  11,  1886. 
WM.  H.  WAHL,  ESQ.,  Secretary  FRANKLIN  INSTITUTE  of  Pennsylvania, 

Philadelphia,  Pa. 

DEAR  SIR:  —  I  make  the  object  of  this,  to  reply  to  your  favors  of 
the  4th  inst  Jn  1871,  the  locomotive  department  of  this  company 
adopted  what  is  known  as  the  United  States,  or  FRANKLIN  INSTITUTE 
Standard,  for  Diameters  and  Threads,  and  have  continued  to  use  it  up 
to  the  present  time.  We  have  experienced  no  particular  difficulty  in 
the  interchanging  of  nuls.  Should  there  be  any  difficulty  in  maintain- 
ing the  straight  surfaces  of  the  threads  more  than  those  of  the  Whit- 
worth  type,  it  would  in  our  opinion  be  more  than  counterbalanced  in 
costing  less  to  maintain  the  straight  surfaces  than  the  curved.  We 
are  of  opinion,  however,  that  the  Whitworth  thread  is  the  strongest, 
i.  e.j  less  liable  to  fracture  the  bolt. 
I  am,  yours  truly, 

I.  M.  LOWRY,  General  Master  Mechanic. 


Chicago,  Rock  Island  &  Pacific  Railway,  Master  Mechanic's  Office. 

CHICAGO,  December  15,  1886. 

WM.  H.  WAHL,  ESQ.,  Secretary  FRANKLIN  INSTITUTE,  Philadelphia,  Pa. 
DEAR  SIR:  —  About  three  years  ago  we  adopted  the  United  States 
Standard  Thread  for  Bolts  and  Nuts,  and  have  so  far  experienced  no 
difficulty  whatever  in  practically  maintaining  the  form  of  the  thread. 
I  have  not  yet  seen  a  case  where  a  bolt  had  worn  so  that  nuts  were 
not  interchangeable. 

I  have  had  very  little  experience  with  the  Whitworth  thread,  but 
feel  certain  that  any  slight  advantage  in  durability  or  strength  which 
it  may  have. over  the  United  States  standard,  is  far  outweighed  by  the 
inconvenience  in  its  construction.  Regretting  that  I  cannot  give  you 
more  scientific  and  interesting  data,  I  am, 
Yours  truly, 

THOS.  B.  TWOMBLY,  General  Master  Mechanic. 


102 

Chicago,  Burlington  &   Quincy  Railroad  Company,  Office  Superintendent 

Motive  Power. 

AURORA,  ILL.,  January  5,  1887. 

FRANKLIN   INSTITUTE    of   Pennsylvania,    WM.    H.    WAHL,    Secretary, 
Philadelphia,  Pa. 

DEAR  SIR:  —  Yours  of  the  4th  duly  received,  asking  whether  this 
road  has  adopted  the  United  States  Standard  thread,  and.  whether  we 
have  experienced  any  difficulty  in  maintaining  the  form  of  the  thread. 

The  United  States  Standard  or  FRANKLIN  INSTITUTE  thread  was 
adopted  in  the  car  department  of  the  Chicago,  Burlington  &  Quincy, 
in  1883,  and  since  then  has  been  gradually  introduced  into  the  loco- 
motive and  track  departments.  For  two  years  past  we  have  used  this 
thread  for  all  purposes.  We  have  had  no  difficulty  whatever  in  main- 
taining the  form  of  the  thread,  that  is  to  say,  we  can  forward  to  any 
point  on  our  line  new  nuts,  which  can  be  used  satisfactorily  on  old 
bolts.  Our  foremen  all  speak  highly  of  the  United  States  Standard, 
owing  to  the  facility  of  maintaining  a  uniform  shape. 

One  of  our  foremen  at  Burlington,  Mr.  Scholey,  who  has  used  the 
Whit  worth  thread  in  the  old  country,  and  the  United  States  Standard 
in  this  country,  says  the  latter  is  much  more  easily  maintained. 

We  enclose  you  some  correspondence  from  our  master  mechanics 
on  this  matter. 

J.  West,  M.  M.,  Burlington  Shop. 

L.  E.  Johnson,  M.  M.,  Aurora. 

C.  F.  Geyer,  General  Foreman  Aurora  Shop. 

Yours  truly,  G.  W.  RHODES,  Supt.  M.  P. 

Chicago,  Burlington  &    Quincy  Railroad   Company,  Locomotive  and   Car 

Department. 

WEST  BURLINGTON,  December  16,  1886. 
G.  W.  RHODES.  ESQ.,  Superintendent  Motive-Power, 

DEAR  SIR:  Referring  to  attached  letters  in  regard  to  screw-threads, 
I  fully  agree  with  Messrs.  Johnson  and  Geyer  in  the  matter  of  threads. 
I  have  talked  this  matter  over  with  our  general  foreman,  Mr.  Scholey, 
and  he  says  that  with  our  American  or  United  States  Standard,  it  is 
much  easier  to  keep  up  taps  and  dies  than  with  the  Whitworth  thread 
with  rounded  edges  and  angles,  which  he  used  in  the  old  country,  and 
a  good 'fit  is  easier  to  make. 

Yours,  J.  WEST. 

Nuts.  —  United  States  Standard  vs.  Whitworth  Thread. 


103 

Chicago,    Burlington    &   Qaincy   Railroad    Company,    Master  Mechanic's 

Office. 

AURORA,  ILL.,  December  11,  1886. 
G.  W.  RHODES,  ESQ.,  Superintendent  M.  P.,  Aurora. 

DEAR  SIR:  —  Returning  your  communication  from  the  FRANKLIN 
INSTITUTE,  and,  in  reply  to  the  same,  would  respectfully  state  that  the 
United  States  Standard  thread  has  been  in  use  in  the  car  department 
since  1883.  During  that  time,  we  have  experienced  no  difficulty  what- 
ever in  practically  maintaining  the  form  of  the  thread  ;  that  is  to  say, 
that  we  can  forward  to  any  point  a  supply  of  new  nuts,  which  can  be 
used  on  bolts  that  have  been  in  service  since  that  time. 

Foremen  of  other  shops  substantiate  Mr.  Geyer's  statement,  that  it 
is  much  more  difficult  to  maintain  the  curved  surface  of  the  Whitworth 
thread  than  the  straight,  or  United  States  Standard.  We  have  no 
absolute  data  on  this  subject,  other  than  practical  experience  for  the 
past  three  years.  We  are  gradually  changing  the  thread  of  bolts  in 
all  departments  to  the  straight,  or  United  States  Standard.  In  doing 
this,  we  experience  no  difficulty  or  annoyance,  as  the  men  in  each  de- 
partment keep  a  small  quantity  of  old  nuts  with  the  old  thread,  so  as 
to  avoid  throwing  away  bolts. 

We  undoubtedly  shall  eventually  have  nothing  but  the  United  States 
Standard  thread  in  use  in  all  departments. 

I  enclose  you  copy  of  Mr.  Geyer's  report. 

Yours  respectfully,       L.  E.  JOHNSON. 


AURORA,  ILL.,  December  9,  1836. 
L.  E.  JOHNSON,  ESQ.,  Div.  M.  M.,  Aurora. 

DEAR  SIR  :  — In  regard  to  the  enclosed,  it  is  my  opinion  that  the 
Whitworth  Standard  tap  is  very  impracticable,  as  it  is  a  hard  matter 
to  make  them  twice  alike,  therefore,  much  more  expensive.  It  is  true, 
if  a  nut  and  bolt  is  in  constant  use,  it  will  wear  about  the  shape  of  the 
Whitworth  Standard,  and  it  may  be  more  durable.  We  have  never, 
as  yet,  experienced  any  trouble  with  the  United  States  Standard 
thread.  A  new  nut  can  always  be  substituted  where  an  old  one  of  the 
same  size  is  taken  off. 

It  will  cost  at  least  double  to  maintain  the  tools  of  the  round  or 
Whitworth  thread,  and,  it  is  my  opinion,  it  is  not  any  better  or' 
stronger  than  the  straight  or  United  States  Standard  thread. 

Respectfully  yours,         [Sgd.]  C.  F.  GEYER. 


104 


SUBJECT STANDARD     SCREW-THREADS. 

The  Pennsylvania  Railroad  Company,  Office  of  General  Superintendent  of 

Motive  Power. 

ALTOOXA,  PA.,  December  20,  1886. 

WILLIAM  H.    WAHL,  ESQ.,   Secretary  FRANKLIN  INSTITUTE,  Philadel- 
phia. Pa. 

DEAR  SIR  :  —  In  reply  to  your  letter  of  December  3d,  would  say, 
that  in  our  experience  we  have  had  no  trouble  at  all  in  maintaining 
the  form  of  thread  of  the  United  States  Standard,  and  the  nuts  we  tap 
are  perfectly  interchangeable. 

We  think  the  straight  surfaces  are  much  more  easily  maintained 
than  the  curved  ones  of  the  Whitworth  thread  would  be,  for  the  rea- 
son that  it  is  easier  to  discover  irregularities  in  straight  than  in  curved 
lines,  and  it  is  quite  easy  to  grind  a  thread  cutting-tool  to  the  straight 
lines  of  the  standard  thread. 

Yours  truly, 

THEO.   N.  ELY,  General  Superintendent  Motive  Power. 


Tke    New     York    Central   &   Hudson  River    Railroad    Company.      Office 

Superintendent  Motive  Power  and  Rolling   Stock.     Room  IJf,  Giand 

Central  Station. 

WM.  BUCHANAN,  Superintendent. 

NEW  YORK,  December  20,  1886. 
WM.  H.  WAHL,  ESQ.,  Secretary  FRANKLIN  INSTITUTE.  Philadelphia,  Pa. 

DEAR  SIR  :  —  In  answer  to  your  inquiry  of  4th  inst.,  we  adopted  the 
United  States  Standard  form  of  thread  three  (3)  years  ago,  and  have 
never  experienced  any  difficulty  in  maintaining  the  form  of  the  threads 
or  in  making  nuts  interchangeable. 

For  durability,  think  the  Whitworth  thread  is  the  best,  but  for  ordi- 
nary work,  think  this  feature  is  offset  by  the  difficulty  in  reproducing 
it. 

The  facility  with  which  the  straight  threads  can  be  produced  by  an 
ordinary  workman  with  tools  that  can  be  readily  made  and  main- 
tained, so  as  to  conform  to  the  standard  guages,  is  a  recommendation 
sufficient  in  itself. 

Yours  truly,  WM.  BUCHANAN. 


105 

2?ew  York,  Lake  Erie   &    Western   Railroad    Company,    Office   Superin- 
tendent of  Motive  Power. 

BUFFALO,  N.  Y.,  February  8,  1887. 

WILLIAM  H.  WAHL,   ESQ.,    Secretary   FRANKLIN  INSTITUTE,    Philadel- 
phia, Pa. 

DEAR  SIR  :  —  In  answer  to  yours  of  December  4th,  ult.,  making 
inquiry  in  regard  to  the  Standard  Screw-Thread  recommended  for 
general  adoption  by  FRANKLIN  INSTITUTE  in  1861.  in  comparison  with 
the  Whit  worth  thread,  would  say  that  we  have  made  careful  inquiry 
in  regard  to  this  matter  from  all  our  master  mechanics  and  foremen 
of  car-repair,  and  the  general  opinion  is  about  as  follows  : 

There  is  little  question  about  the  practical  superiority  of  the  Sellers, 
or  United  States  Standard  Thread. 

The  principal  differences  between  the  two  are  in  the  angle  of  the 
thread  and  the  form  at  top  and  root  of  thread. 

The  angle  of  the  Sellers  thread  is  more  easily  maintained  than  the 
other,  because  a  templet  can  be  accurately  made  without  the  use  of 
special  tools,  as  it  is  easy  to  construct  the  angle  geometrically.  It  is 
also  simpler  and  cheaper  to  cut  the  Sellers  thread  in  a  lathe.  It  is  a 
difficult  matter  to  make  the  nut  fit  closely  on  the  curved  portion  of  the 
Whitworth  thread,  and  practically  the  bearing  surface  will  probably 
be  limited  to  the  straight  parts,  making  it  considerably  less  than  in  the 
Sellers  system,  consequently  more  liable  to  be  distorted  as  far  as  this 
element  goes. 

We  have  no  trouble  arising  from  the  wear  of  the  United  States 
Standard  tap  sufficient  to  prevent  the  nuts  from  being  interchangeable. 

Yours  truly, 
RICHARD  H.  SOULE,  Superintendent  Motive  Power. 

T. 

The  Pratt  &  Whitney  Company,  Manufacturers  of  Machinists''  Tools. 

HARTFORD,  CONN.,  U.  S.  A.,  December  29,   1886. 
DR.  WM.  H.  WAHL,  Secretary  FRANKLIN  INSTITUTE,  Philadelphia,  Pa. 

DEAR  SIR  :  —  Your  favor  of  the  28th  inst.,  is  to-day  received.  We 
trust  you  will  pardon  us  for  the  delay  in  complying  with  your  esteemed 
request  of  the  4th  inst.,  mainly  due  to  absence  of  the  writer  to  whom 
the  matter  was  referred,  and  the  subsequent  unusual  demands  upon 
his  time. 

Regarding  our  experience  as  manufacturers  of  taps  and  dies,  espe- 
cially those  covering  the  application  of  the  Sellers  System  of  Screw-. 


106 

Threads,  now  known  as  the  FRANKLIN  INSTITUTE  or  United  States 
Standard,  we  can  say,  as  stated  in  our  letter  to  the  Railroad  Gazette, 
and  published  in  their  issue  of  September  24,  1886,  included  in  article 
on  "  Screw-Threads,"  that  the  orders  we  have  received  for  taps  and  dies 
from  railroad  companies,  bolt  manufacturers,  bridge  builders,  and  man- 
ufacturers generally,  in  the  United  States,  are  largely  for  the  United 
States  Standard  thread.  Fully  ninety  per  cent,  are  strictly  so,  and 
many  of  the  others  not  United  States  Standard  both  in  form  of  thread 
and  pitch,  are  so  in  shape  of  the  thread,  i.  e.,  flat  at  top  and  bottom  one- 
eighth  of  the  pitch,  and  having  a  greater  number  of  threads  per  inch. 
This  is  necessary  for  special  cases,  such  as  tool  work  and  small  diame- 
ter taps  and  bolts. 

The  form  of  the  Sellers,  FRANKLIN  INSTITUTE  or  United  States 
Standard  thread,  is  such  as  to  make  it  the  most  practicable  for  dupli- 
cation to  guage,  and  by  making  the  outside  diameter  slightly  larger 
(not,  however,  larger  in  the  angle  of  the  thread),  the  life  of  the  tap  or 
before  it  wears  below  guage  size,  is  greatly  lengthened. 

The  claim  that  the  form  of  the  Sellers  thread  cannot  be  maintained 
in  use,  seems  in  our  experience  inadmissible,  for  although  the  corners 
may  wear  slightly,  this  wear  is  unimportant  if  the  taps  are  properly 
used,  and  especially  so,  if  made  as  recommended  —  slightly  larger  in 
the  outside  diameter. 

Our  position  in  the  matter  is  stated  more  fully  in  the  article  pub- 
lished in  the  Railroad  Gazette,  referred  to,  and  should  you  desire 
further  information,  we  shall  be  glad  to  be  of  service  to  you  if  in  our 
power. 

Regretting  the  delay,  we  are, 

Tours  respectfully, 

THE  PRATT  &  WHITNEY  COMPANY, 
GEO.  M.  BOND,  Manager  Gauge  Department. 

[Following  is  the  article  from  the  Railroad  Gazette,  September  24, 
1886,  referred  to  in  Mr.  Bond's  letter.] 


SCREW-THREADS. 

The  last  issue  of  Engineering  publishes  an  article  on  "  Screw- 
Threads,"  chiefly  dealing  with  a  movement,  in  Germany,  to  abandon 
the  Whitworth  Standard  for  a  new  one  based  on  metric  measures,  in 
which  some  very  large-sized  and  strangely  erroneous  statements  are 


107 

made  in  reference  to  what  has  now  become  the  American  Standard  — _ 
The  Sellers  thread.  It  says  : 

"  The  form  of  cross-section  Whit  worth  adopted  for  ordinary  pur- 
poses, was  that  of  a  triangle,  whose  height  was  0.96  of  the  pitch  and  the 
angle  at  the  bottom  of  the  threads  55°  ;  one-sixth  of  these  triangular 
sections  was  rounded  off  at  the  top  and  bottom.  This  system  has  been 
very  widely  and  almost  universally  used  for  the  last  thirty  years,  the 
chief  and  only  important  exception  to  their  universality  being  in  the 
United  States,  where  Sellers  threads  are  very  much  used  :  they  are  of 
a  slightly  different  pitch  and  form  of  cross-section,  being  an  equilat- 
eral triangle  with  one  eighth  of  the  depth  cut  off  square,  both  top  and 
bottom. 

"The  objection  (to  the  form  of  the  Whitworth  thread)  is  totally 
unjustifiable,  for  thirty  years  of  practice  have  most  unmistakably 
proved  the  Whitworth  form  of  cross-section  to  be  the  best ;  the  square- 
tipped  thread,  on  the  other  hand,  as  advocated  by  the  metrical  sys- 
tem, has  proved  unsuccessful.  It  has  been  thoroughly  tried  by 
Sellers  in  the  United  States,  where  it  has  been  found  practically  im- 
possible to  produce  a  good  thread  by  screwing  apparatus,  the  sharp 
corners  on  the  taps  and  dies  rapidly  break  away,  when  a  very  imper- 
fect thread  must  naturally  follow.  The  present  state  of  affairs  in 
America  conclusively  shows  the  system  to  be  a  failure,  and  all  the 
leading  machine  tool-makers  there  are  supplying  nothing  but  the 
V-shaped  thread  very  similar  to  Whitworth's." 

The  Sellers  threads  are,  indeed,  "  very  much  used,"  as  they  are  the 
standards  of  the  United  States  army  and  navy,  and  of  the  Master 
Mechanics'  and  Master  Car-Builders'  Associations,  and  of  most  of  the 
large  railroad  shops  at  least.  That  "all"  the  leading  tool-makers  are 
supplying  "  nothing "  but  the  V-thread  "  very  similar  to  Whit- 
worth's,"  is  a  fabrication,  by  some  one,  out  of  the  whole  cloth.  The 
facts  of  the  case  are,  that  from  eighty  to  ninety  per  cent,  of  the  taps 
and  dies  sold  by  various  dealers  are  already  of  the  Sellers  Standard, 
and  the  remainder  of  a  plain  V-thread,  the  latter  having  been  form- 
erly universal,  and  being  still  quite  largely  used,  taking  the  whole 
United  States  together.  That  the  Sellers  Standard  is,  in  any  sense 
of  the  word,  going  out  —  and  still  less  that  it  has  practically  gone 
out,  as  Engineering  explicitly  asserts  —  is  utterly  untrue.  On  the  con- 
trary, it  is  coming  in.  There  is  little  room  for  doubt  that  its  use 
is  becoming  more  general  every  day,  and  it  would  now  be  hard  to 
find  a  railroad  anywhere  on  which  it  would  not  be  asserted,  at  least, 
that  the  Sellers  (or  "M.  C.  B.,"  or  "United  States,"  as  it  is  variously 


108 

known)  Standard  was  in  use.  Many  more  will  assert  that  they  use  it 
than  actually  do  use  it,  but  that  is  natural. 

The  comparative  merits  of  the  Whitworth  and  Sellers  Standards  we 
are  not  discussing.  This,  however,  we  may  say,  that  records,  as 
respects  durability  and  adherence  to  standard,  are  being  made  every 
day  with  taps  aijd  dies  of  the  Sellers  Standard,  which  certainly  have 
not  been,  and  probably  cannot  be,  surpassed  or  even  approached. 
The  " sharp"  angles  (120°)  do  not,  so  far  as  we  have  ever  heard,  or 
can  learn,  give  any  difficulty  from  breaking  off,  while  they  do  enable 
the  standard  to  be  exactly  reproduced  and  readily  maintained,  so  that 
complete  interchangeability  is  assured.  As  it  now  appears  quite  cer- 
tain that  it  will  come  into  practically  universal  use  in  America,  and  as 
there  is  no  prospect  that  any  other  standard  will,  anything  calculated 
td  impede  its  so  far  continuous  progress  to  that  end  is  greatly  to  be 
regretted.  Fortunately,  Engineering's  assertions  are  so  exaggerated, 
and  —  to  anyone  familiar  with  American  practice  —  palpably  false, 
that  they  are  calculated  to  disprove  themselves. 

To  make  assurance  doubly  sure  in  this  matter,  we  addrersed  an 
inquiry  to  The  Pratt  &  Whitney  Company  of  Hartford,  Conn  ,  famous 
throughout  this  continent,  and,  we  should  imagine,  throughout  the 
world,  not  only  for  the  magnitude  and  excellence  of  their  products, 
but  for  their  exertions  and  success  in  turning  out  minutely  exact 
standards  of  various  kinds,  and  especially  for  screw-threads.  We 
risk  little  in  saying  that  no  house  in  the  world  is  better  qualified  by 
experience  to  form  correct  conclusions  in  such  a  matter.  The  follow- 
ing is  their  reply: 

"  Referring  to  Engineering's  comments  on  the  second  objection 
brought  up  by  the  commission  and  the  Karlsruhe  Society  against  the 
Whitworth  thread,  viz.: 

"  '  (2.)  The  Whitworth  system  being  measured  in  inches,  it  is  incon- 
venient for  metrical  measurements,'  and  the  reply  by  the  author  of 
the.  article  in  Engineering  referred  to,  which  is  as  follows  : 

" '  If  a  new  universal  system  of  screw-threads  must  be  adopted, 
then  it  should  not  be  tied  down  to  any  special  system  of  measurement, 
but  should  rather  be  designed  on  a  system  of  standard  gauges  of 
various  grades,  similar  to  our  Birmingham  wire-gauge  system,' 

"  We  would  say  that  if  the  writer  had  been  aware  of  the  fact  that 
the  British  Board  of  Trade  had  established  in  decimal  sizes  all  Bir- 
mingham gauge  dimensions  —  in  effect  on  and  after  March  1,  1884  — 
he  would  not  have  made  the  assertion  there  given. 

"  In  regard  to  the  disposal  by  Engineering  of  the  third  objection  to 


109 

the  Whitworth  thread  raised  by  the  Karlsruhe  Society,  viz.  (that  it  is 
difficult  of  manufacture),  a  method  of  disposal  which  has  justly  aroused 
your  indignation  and  our  own,  we  can  also  say  that  the  Sellers  or 
FRANKLIN  INSTITUTE  thread,  now  generally  known  as  the  United 
States  Standard,  is  in  every  respect  a  more  practical  form  of  thread 
to  maintain  to  gauge  than  the  old  V -thread,  or  even  the  Whitworth, 
and  is  a  much  more  simple  thread  to  produce  by  machinery  or  the 
ordinary  work-shop  tools  than  the  latter  form. 

"  As  to  the  Sellers  thread  being  a  'failure,'  we  will  only  refer  to  the 
fact  that  in  our  large  and  increasing  production  of  taps  and  dies  for 
the  market  in  this  country,  ninety  per  cent,  are  United  States  Standard, 
while  many  not  strictly  United  States  Standard  in  number  of  threads 
per  inch,  are  so  in  form  of  thread,  i.  e.,  one-eighth  of  the  pitch  flat, 
top  and  bottom. 

"  V-threads  and  over-size  threads  are  not  used  to  the  extent  they 
once  were,  thanks  to  the  untiring  devotion  of  the  Master  Car-Builders' 
Association,  through  their  committee  having  this  matter  in  charge; 
for  it  is  now  an  accomplished  fact  that  bolts  and  nuts  are  interchange- 
able throughout  the  United  States,  which  was  not  possible  under  the 
old  system  of  V  and  over-size  threads. 

"Furthermore,  a  United  States  Standard  tap  made  in  the  proper 
manner  will  cut  ten  times  as  many  nuts  as  wiJl  one  with  the  simple 
V-thread,  without  appreciable  change  of  size  as  compared  with  a  stand- 
ard gauge. 

"  The  United  States  Standard  form  of  thread  embodies  a  condition 
which  makes  this  great  lengthening  of  the  life  of  a  tap  possible,  and 
this  is  not  nearly  so  easily  accomplished  in  the  Whitworth  thread. 
At  all  events,  it  is  impracticable  in  the  latter  form  to  carry  out  the 
conditions  referred  to,  and  an  impossibility  in  the  V-thread. 

"As  to  the  objection  regarding  relative  strength  of  the  bolt  cut  with 
the  United  States  Standard  or  the  Whitworth  thread,  we  can  refer  to 
the  United  States  Navy  Board  report  of  May  9,  1868,  which  certainly 
.shows  this  objection  to  be  unfounded. 

"THE  PRATT  &  WHITNEY  COMPANY. 
("GEO.  M.  BOND,  Manager  Gauge  Department") 


This  is  not  the  first  time  that  facts  and  figures  as  to  American  prac- 
tice have  been  "evolved  from  the  inner  consciousness"  of  writers 
across  the  water,  to  suit  the  occasion,  but  it  is  not  often  that  such  a 
complete  perversion  and  reversal  of  the  facts  is  given  currency  in  a 


110 

journal  of  standing.  In  addition  to  the  railroad  shops,  the  Baldwin 
Locomotive  Works,  and  nearly,  if  not  quite,  all  the  other  large  loco- 
motive shops,  are  using  the  Sellers  system,  as  are  also  most  of  the  car 
shops.  Hoopes  &  Townsend  of  Philadelphia,  the  largest  single  manu- 
facturers of  track  bolts,  are  also  using  it.  The  prospects  are  excellent 
that  the  system  will  come  into  universal  use,  as  it  is  now  in  large  and 
rapidly  increasing  use.  A  correction  would,  therefore,  seem  to  be  in 
order.  —  Railroad  Gazette,  Sept.  2Jk  1886. 


I  have  taken  this  method  of  replying  to  your  inquiry  as  best  cal- 
culated to  answer  such  allegations  as  are  made  in  (London)  Engi- 
neering, of  September  10,  1886,  and  have  only  to  add,  that,  from 
the  letters  and  publications  above  referred  to,  it  must  be  evident 
that  the  Sellers  or  FRANKLIN  INSTITUTE  Standard  for  pitches  and 
form  of  thread  is  accepted  and  used  throughout  the  United 
States,  to  the  exclusion  of  any  other ;  that  is  to  say,  while  there 
are  still  some  parties  who  have  not  adopted  any  standard,  there 
are  none  who  have  adopted  any  other  standard  than  the  Sellers. 

Hoping  you  may  find  the  information  herewith  forwarded  to 
be  a  satisfactory  answer  to  your  inquiries,  I  have  the  honor  to 
remain,  Yours  respectfully, 

WM.  H.  WAHL,  Secretary. 


[Reprinted  from  the  JOURNAL  OF  THE  FRANKLIN  INSTITUTE,  April,  1884, 
with  Revision  by  the  Author,  June,  1887.] 


STANDARDS  OF  LENGTH  AND  THEIR  SUBDIVISION. 

BY 

GEORGE  M.  BOND,  Hartford,  Conn. 
[A  lecture  delivered  before  the  FRANKLIN  INSTITUTE,  February  21,  1884.] 


We  are  all,  no  doubt,  familiar  with  the  old  table  of  English 
measures  of  length  beginning  "  three  barleycorns  make  one  inch." 
I,  for  one,  can  remember  having  vague  ideas  in  regard  to  barley- 
corns in  general,  and  their  exact  size  in  particular,  though  I 
imagined'!  knew  exactly  what  constituted  an  inch.  Later  in  life 
I  began  to  doubt  my  knowledge  in  this  respect,  having  had  con- 
siderable difficulty  in  reconciling  the  differences  between  two 
separate  inches  not  exactly  alike,  one  of  which  evidently  was  not 
3^  part  of  a  standard  yard. 

It  may  be  of  interest  to  glance  over  the  history  of  the  gradual 
development  of  the  modern  science  of  minute  measurement,  to 
notice  how  such  crude  standards  as  the  human  foot  or  arm,  and 
standards  called  cubits,  fathoms,  or  the  foot  made  up  of  "  thirty- 
six  barleycorns,  round  and  dry,  placed  end  to  end,"  in  the  course 
of  time  grew  into  the  more  exact  determinations  of  scientific 
research,  as  shown  in  the  results  of  the  labors  of  men  like  Kater, 
Baily,  Bessel,  Sheepshanks,  Shuckburgh,  and  Sir  George  Airy  in 
the  great  problem  of  establishing  a  standard  of  length  from  a 
natural  unit.  They  gave  us  so  closely  the  relation  of  the  length 
of  a  pendulum  beating  seconds  of  time  to  the  length  of  a  yard, 
that  it  was  thought  they  had  determined,  beyond  further  doubt, 
the  means  for  restoring  a  lost  standard  should  it  become  neces- 
sary to  do  so  from  any  cause. 

However  good  these  crude  standards,  such  as  a  barleycorn,  a 
human  arm  or  foot,  may  have  been  for  practical  purposes  at  the 
time  they  were  adopted,  they  certainly  are  in  our  times  com- 


112 

pletely  out  of  the  question  and  useless  for  precise  determina- 
tions. As  all  measures  derived  from  them  were  purely  arbi- 
trary and  sanctioned  by  law,  no  reference  made  to  any  of  these 
sources  could  be  presumed  to  restore  a  lost  original  standard, 
even  such  as  a  common  yard-stick,  except  within  a  very  liberal 
margin  of  error;  we  need  not  be  surprised  to  find  that  there 
happened  such  a  wide  range  of  value  for  a  foot  as  that  of  the 
Pythic  of  9f  inches  to  that  of  Geneva  of  19  inches. 

The  adoption  of  an  invariable  unit  as  a  standard  of  length, 
while  seemingly  only  applicable  to  the  refined  methods  of  science, 
really  becomes  a  necessity  in  our  ordinary  workshop  practice,  as 
we  shall  see  later  on  in  our  presentation  of  this  subject. 

The  arm  of  King  Henry  the  First,  or  the  barleycorn,  though 
possibly  furnishing  a  standard  good  enough  at  that  time,  would 
hardly  satisfy  the  requirements  of  our  modern  mechanics  or  tool- 
makers,  who  work  very  often  within  the  limit  of  a  thousandth  of 
an  inch,  and  even  one-tenth  of  this  apparently  minute  quantity, 
with  surprising  unconcern  and  no  less  accuracy. 

To  the  celebrated  philosopher  and  scientist  Huyghens  is  due 
the  honor  of  having  demonstrated  the  principle,  that  the  times  of 
the  vibrations  of  pendulums  depend  entirely  upon  their  length. 
About  the  year  1670  his  inventive  genius  conceived  the  plan  of 
using  this  fact  to  establish  the  length  of  a  standard  which  should 
be  the  unit  for  measures  of  length.  This  he  divided  into  three 
equal  parts,  each  of  about  thirteen  inches,  calling  this  third  part 
the  "  horary  foot." 

Picard,  in  1671,  also  proposed  using  the  length  of  a  pendulum 
beating  seconds  of  mean  time,  which  should  be  adopted  as  the 
unit  of  length,  thus  endorsing  the  plan  of  Huyghens.  It  was 
Picard  who  first  measured  the  arc  of  the  meridian  from  Paris  to 
Amiens,  in  1669,  deducing  from  it  the  value  of  a  degree  to  be 
68.945  miles.  Picard  was  the  first  to  suggest  that  the  diurnal 
revolution  of  the  earth  necessarily  affected  the  times  of  oscilla- 
tion of  a  seconds  pendulum,  and  that  it  ought  to  vibrate  more 
rapidly  at  the  poles  than  at  the  equator.  His  experiments  at 
different  latitudes,  howevor,  failed  to  confirm  this  theory,  probably 
owing  to  the  lack  of  sufficiently  accurate  apparatus  for  his  work, 
and  it  was  left  to  Richer,  in  the  same  year,  (1671,)  to  prove  that, 
at  the  equator,  or  4°  56'  north,  where  the  observations  were 


113 

made,  the  difference  of  the  length  of  a  seconds  pendulum  at  that 
place,  as  compared  with  the  length  at  Paris,  or  48°  50'  north, 
was  about  a  line  and  a  quarter,  or  over  one-tenth  of  an  inch. 

Cassini,  in  1718,  proposed  a  unit  which  should  be  ^00-  Pai>t  of 
a  minute  of  a  degree  of  a  great  circle  of  the  earth,  and  which 
would  be  nearly  equal  to  a  third  part  of  our  yard.* 

M.  de  la  Condirnine,  who  had  measured  a  degree  at  the  equa- 
tor in  Peru,  in  a  Memoir  read  before  the  Academy  of  Sciences 
at  Paris,  advocated  the  use  of  a  pendulum  as  the  unit  of  length, 
proposing  that  it  should  beat  seconds  at  the  equator,  a  place 
least  likely  to  cause  prejudice  that  might  follow  national  jeal- 
ousy, were  the  latitude  of  any  particular  place  selected. 

Talleyrand,  in  1790,  proposed  to  the  Assembly  of  France  that 
a  commission  be  appointed  to  consult  with  a  similar  commission 
from  the  English  government,  to  consider  the  subject  of  a  uni- 
form international  system  of  metrology.  He  favored  the  length 
of  a  pendulum  as  compared  with  the  unit  obtained  by  the  subdi- 
vision of  a  quadrant  of  the  earth's  meridian ;  but  after  a  careful 
consideration  of  the  three  plans  proposed, —  the  pendulum,  a 
quarter  of  the  equator,  and  a  quadrant  of  the  earth's  meridian, — 
they  concluded  to  recommend  the  latter  method. 

In  1790,  one  year  before  the  International  Commission  had: 
adopted  the  ten-millionth  part  of  the  quadrant,  as  settling  the 
question  of  a  natural  unit  for  a  standard  measurement  of  length, 
and  before  any  steps  had  been  taken  by  them  in  the  matter,.. 
Thomas  Jefferson,  then  Secretary  of  State,  in  obedience  to  a  reso- 
fution  of  Congress  calling  upon  the  Secretary  to  propose  a  plan, 
for  establishing  a  uniformity  in  the  currency,  weights,  and  meas- 
ures for  the  United  States,  recommended,  in  his  report,  a  deci- 
mal system  of  metrology,  and  that  the  unit  be  derived  from  a. 
natural  and  invariable  standard  of  length. 

Jefferson  considered  that  though  the  globe  or  its  great  circles- 
might  be  invariable,  the  means  to  be  employed  to  obtain  an, 
accurate  subdivision  of  a   quadrant   from   previous   trials   had 
showed  their  unreliability  and  promised  too  great  a  degree  of 
uncertainty ;  he  therefore  objected  to  the  ordinary  form  of  the 

*  Report  on  Weights  and  Measures,  by  Dr.  Alfred  B.  Taylor,  Eighth  Annual  Session,  Phar. 
maceutical  Association,  Boston,  September  15,  1859. 
8 


114 

pendulum,  as  "  not  without  its  uncertainties,"  the  length  not 
being  possible  to  be  accurately  determined,  owing  to  variations 
in  the  clock-work  mechanism  and  to  barometric  and  thermo- 
metric  variations.  He  recommended  the  latitude  of  45°  and  a 
mean  temperature  of  the  year  at  that  location. 

Instead  of  using  the  ordinary  pendulum  of  thirty-nine  inches, 
he  advised  the  use  of  a  seconds  rod  of  five  feet,  known  as  Leslie's 
pendulum  rod. 

This  was  a  simple  straight  bar,  without  a  disc  or  bob,  sus- 
pended at'  one  end,  and  free  to  swing  at  that  point,  its  center  of 
oscillation  being  at  a  distance  of  two  thirds  of  its  length  from 
the  point  of  suspension.  It  would  be  one-half  longer  than  the 
ordinary  loaded  pendulum. 

A  rod  of  this  kind,  vibrating  seconds,  is  58.72  inches  long. 

He  proposed  that  this  rod  be  made  of  iron,  of  such  a  length 
that  at  a  level  of  the  sea,  at  a  latitude  of  45°,  and  with  a  con- 
stant temperature,  it  should  beat  seconds  of  mean  time ;  its 
length,  given  exactly,  would  be  58.72368  inches. 

Jefferson  then  proposed  dividing  this  length  into  five  equal 
parts,  calling  each  part  a  foot,  which  would  give  11.74473  inches 
as  the  length  of  the  new  foot.  He  then  divided  the  foot  into  ten 
equal  parts,  affording  a  decimal  subdivision  to  correspond  with 
the  decimal  character  of  the  coinage  of  the  country. 

The  French  Commission,  after  carefully  determining  the 
length  of  a  quadrant  of  the  earth's  meridian,  and  dividing  it  into 
ten  million  equal  parts,  presented  science  and  the  world  with  the 
meter  as  a  universal  standard  to  which  posterity  might  ever 
afterward  refer.  Its  length,  as  they  computed  it,  is  very  nearly 
the  length  of  the  seconds  pendulum,  or  39.370788  inches,  or 
nearly  3f  inches  longer  than  the  yard. 

This  meter,  which  is  an  end-measure  standard,  was  made  of 
an  alloy  of  platinum  and  iridium,  ninety  parts  of  the  former  to 
ten  of  the  latter.  It  is  called  the  "Metre  des  Archives,"  and  is 
kept  in  the  buildings  of  the  International  Bureau,  at  Breteuil, 
between  Paris  and  Versailles. 

Having  thus  briefly  touched  upon  the  history  of  individual 
and  national  efforts  to  secure  a  unit  for  a  standard  of  length, 
.covering  a  period  of  about  two  hundred  years  preceding  the 
.legal  adoption  of  our  standard  yard,  it  may  be  interesting  to 


115 

know  that  just  five  hundred  years  after  the  statute  of  17th, 
Edward  II,  A.  D.  1324,  which  enacted  that  "  three  barleycorns, 
round  and  dry,"  make  an  inch,  and  twelve  inches  make  one 
foot,  it  was,  by  act  of  5th,  George  IV,  Cap.  74  (1824),  that  a 
legal  definition  of  the  yard  was  made,  and  by  it  was  declared 
that  the  yard-bar,  made  by  Bird  in  1760,  should  be  the  standard 
beyond  any  question  or  doubt.* 

It  may  be  in  place  to  quote  here  an  abstract  of  the  Act  of 
June  17,  1824,  legalizing  this  standard,  and  which  reads  as 
follows: 

SECTION  I.  Be  it  enacted  ....  that  from  and  after  the  first 
day  of  May,  one  thousand  eight  hundred  and  twenty-five,  the 
Straight  Line  or  Distance  between  the  Centers  of  the  Two 
Points  in  the  Gold  Studs  in  the  Straight  Brass  Rod,  now  in  the 
Custody  of  the  Clerk  of  the  House  of  Commons,  whereon  the 
Words  and  Figures  "  Standard  Yard,  1760, "  are  engraved,  shall 
be  and  the  same  is  hereby  declared  to  be  the  Extension  called  a 
Yard ;  and  that  the  same  Straight  Line  or  Distance  between  the 
Centers  of  the  said  Two  Points  in  the  said  Gold  Studs  in  the 
said  Brass  Rod,  the  Brass  being  at  the  temperature  of  Sixty-two 
Degrees  by  Fahrenheit's  Thermometer,  shall  be  and  is  hereby 
denominated  the  "  Imperial  Standard  Yard." 

SECTION  III.  And  whereas  it  is  expedient  that  the  said  Stand- 
ard Yard,  if  lost,  destroyed,  defaced,  or  otherwise  injured,  should 
be  restored  to  the  same  Length  by  reference  to  some  invariable 
natural  Standard  ;  And  whereas  it  has  been  ascertained  by  the 
Commissioners  appointed  by  His  Majesty  to  inquire  into  the 
subject  of  Weights  and  Measures,  that  the  Yard  hereby  declared 
to  be  the  Imperial  Standard  Yard,  when  compared  with  a  Pen- 
dulum vibrating  Seconds  of  Mean  Time  in  the  Latitude  of  Lon- 

O 

don  in  a  Vacuum  at  the  Level  of  the  Sea,  is  in  the  proportion  of 
Thirty-six  Inches  to  Thirty-nine  Inches  and  one  thousand  three 
hundred  and  ninety  three  ten-thousandth  Parts  of  an  Inch;  Be 

*  This  Act  was  introduced  into  the  House  of  Commons  in  1822,  but  failed  to  pass  the  House 
of  Lords.  It  was  again  introduced,  with  modifications,  in  1823,  but  was  not  passed  until  June 
17, 1824,  to  go  into  effect,  as  stated,  May  1,  1825.  This  was,  however,  postponed  to  January  1, 
1826. 

["  Weights  and  Measures,"  by  Prof.  F.  A.  P.  Barnard,  Johnson's  New  Cyclopaedia,  p.  1737, 
Appendix.  See,  also,  Encyclopaedia  Brittanica,  8th  Edition,  Vol.  xxi.,  pp.  803  and  807.] 


116 

it  therefore  enacted  and  declared,  That  if  at  any  Time  hereafter 
the  said  Imperial  Standard  Yard  shall  be  lost  or  shall  be  in  any 
Manner  destroyed,  defaced,  or  otherwise  injured,  it  shall  and 
may  be  restored  by  making  a  new  Standard  Yard,  bearing  the 
same  proportion  to  such  Pendulum  as  aforesaid,  as  the  said 
Imperial  Standard  Yard  bears  to  such  Pendulum. 

Just  ten  years  afterward,  Oct.  16,  1834,  occurred  the  calamity 
for  which  the  carefully  worded  text  of  Section  III  was  intended 
to  provide, —  a  contingency  certainly  most  wisely  considered. 
This  was  the  destruction  of  the  Standard  Yard  by  fire,  when 
both  houses  of  Parliament  were  burned. 

The  bar  was  recovered,  but  in  a  damaged  condition,  and  all 
hopes  of  restoring  its  usefulness  were  abandoned  when  it  was 
found  that  one  of  the  gold  plugs  had  been  melted  out.  The 
provisions  of  the  Act  now  came  into  service,  in  order  to  repro- 
duce the  lost  Standard,  and  it  became  necessary  to  decide  whether 
it  could  be  restored  by  the  use  of  the  method  so  carefully 
prescribed. 

It  has  been  proved  conclusively  since  the  passage  of  the  Act 
that  there  were  errors  in  the  determination  of  the  specific  grav- 
ity of  the  pendulum  employed;  the  reduction  to  the  sea-level 
had  been  shown  by  Dr.  Young  to  have  been  doubtful ;  the  reduc- 
tion for  the  weight  of  air  was  also  proved  erroneous,  and  Kater 
showed  that  sensible  errors  had  been  introduced  in  comparing 
the  length  of  the  pendulum  with  Shuckburgh's  scale,  this  bar 
having  been  compared  with  Bird's  "  Standard,  1760,"  and  found 
to  agree  closely. 

Shuckburgh's  scale,  marked  (0  —  36in),  was  made  by  Troughton 
in  1798,  and  had  been  compared  with  the  pendulum  and  with  the 
meter.  It  may  be  interesting  to  know,  that  previous  to  Shuck- 
burgh,  all  transfers  of  the  yard  were  made  by  the  use  of  beam 
compasses,  and  comparisons  were  also  made  in  the  same  way. 

It  was  not  until  1798  that  optical  instruments  were  used  for 
this  purpose,  and  Troughton  must  be  credited  with  having  intro- 
duced this  wonderfully  improved  manner  of  dealing  with  minute 
measurements,  and  which  afterward,  no  doubt,  led  to  the  discov- 
ery of  the  errors  found  to  have  crept  in  when  the  relation  of  the 
yard  to  the  length  of  the  pendulum  was  originally  established. 


117 

All  attempts,  therefore,  to  use  the  pendulum  for  the  purpose 
of  reproducing  the  lost  standard  were  abandoned.  The  next 
step  was  to  approximate  this  result  by  the  use  of  standards  then 
in  existence,  which  had  been  compared  with  the  original  yard. 

The  bars  used  for  this  purpose  were : 

(a)  Shuckburgh's  Scale  (0  — 36in). 

(b)  Shuckburgh's  Scale,  with  Kater's  authority. 

(c)  The  Yard  of  the  Royal  Society,  constructed  by  Kater. 

(d)  Two  Iron  Bars,  marked  A1  and  J2,  belonging  to  the  Ord- 
nance Department,  and  kept  in  the  Office  of  the  Trigonometrical 
Survey. 

To  Sir  Francis  Baily  was  intrusted  the  work  of  the  restoration 
of  the  yard.  His  death,  unfortunately,  occurred  in  1844,  before 
the  work  was  completed.  He  had  then  only  completed  the  pro- 
visional or  preliminary  investigations  necessary  for  this  most 
important  undertaking. 

.He  had,  however,  made  a  great  many  experiments  to  deter- 
mine the  proper  material  for  the  new  standard,  and  finally 
decided  upon  the  alloy  of  which  Bronze  No.  1  was  afterwards 
made.  It  is  still  known  as  Baily's  metal.  Its  composition  is 
copper  16,  tin  2J,  and  zinc  1. 

The  work  was  now  entrusted  to  the  Rev.  R.  Sheepshanks. 
He  constructed  first,  a  brass  bar  as  a  "  working  standard."  This 
bar  was  compared  with  all  the  standards  considered  by  him  nec- 
essary for  the  purpose,  and  which  were  those  just  mentioned. 
Taking  the  average  of  all  the  values  of  each,  compared  with 
the  brass  bar  No.  2,  as  the  working  standard  was  designated,  and 
reducing  to  an  assumed  value  of  the  original  standard  yard,  he 
found  for  the  relation  of  the  new  yard,  brass  bar  No.  2  =  36.00025 
inches  of  the  lost  Imperial  standard,  taken  at  62°  Fahr.  The 
brass  tubular  scale  of  the  Astronomical  Society  did  not  appear  in 
the  list  of  bars  used  as  references  (see  Phil.  Trans.  1857,  p.  661), 
and  the  statement  that  this  was  the  principal  authority  for  the 
new  standard  is  therefore  incorrect. 

Bronze  19,  as  the  new  yard  was  designated,  or  now  known  as 
No.  1,  was  graduated  according  to  this  value,  in  terms  of  the  lost 
Imperial  standard,  found  from  the'comparison  of  these  five  stand- 
ards, and  is  made,  as  just  stated,  of  Baily's  metal,  the  dimensions 
are:  length  38  inches,  depth  1  inch,  width  1  inch.  The  gradua- 


118 

tions  are  upon  gold  pings  inserted  in  wells  of  sncli  a  depth  as  to 
bring  the  polished  surfaces  of  the  plugs  at  a  distance  from  the  top 
equal  to  one-half  the  depth  of  the  bar,  the  plugs  being  36  inches 
apart. 

The  bar  which  is  here  exhibited,  is  a  copy  in  every  respect, 
except  that  it  has  the  subdivision  of  feet  besides ;  but  we  have 
the  same  material,  the  same  dimensions,  and  the  same  conditions 
in  the  graduations,  while  more  than  all,  the  distance  between  the 
two  defining  lines  as  compared  with  Bronze  No.  1,  varies 
less  than  one  hundred-thousandth  of  an  inch  at  62°  Fahr. 

This  bar  was  constructed  by  Professor  W.  A.  Rogers,  of  Har- 
vard College  Observatory,  Cambridge,  for  The  Pratt  &  Whitney 
Company  of  Hartford,  Conn.,  for  their  use  as  a  final  reference 
standard.  It  has  been  compared  directly  with  Bronze  11,  at  the 
office  of  the  Coast  Survey,  by  Professor  J.  E.  Ililgard  and  Pro- 
fessor Rogers,  and  allowing  for  the  known  relation  between 
Bronze  11  and  Bronze  No.  1,  its  value  was  found  to  be  within 
this  minute  limit,  in  terms  of  the  Imperial  Yard.* 

The  reason  assigned  for  placing  the  lines  at  the  center  of  the 
depth  of  the  bar,  was  to  neutralize  errors  arising  from  flexure 
which  were  liable  to  occur;  that  is,  by  the  bending  of  the  bar, 
the  distance  between  the  lines  would  become  less.  Having  the 
graduations  at  the  center  was  thought  would  neutralize  this 
effect.  We  all  know  that  if  a  beam  is  supported  at  the  ends 
and  loaded  in  the  middle,  the  beam  is  compressed  at  the  top, 
and  stretched  or  extended  at  the  bottom,  and  if  we  were  to 
measure  between  finely  drawn  lines,  before  and  after  the  load 
was  applied,  we  would  find  that  the  lines  were  nearer  together 
when  the  beam  was  under  strain  than  when  free,  measuring,  of 
course,  in  a  straight  line;  hence  it  was  thought  that  having  the 
lines  midway  between  the  top  and  bottom  of  the  standard  bar, 
this  error  would  be  reduced. 

Captain  Kater  was  the  first  to  discover  the  variations  due  to 
the  flexure  of  standard  bars  upon  which  graduations  were  traced, 
and  he  first  proposed  a  "  neutral  plane,"  which  would  have  the 
effect,  within  certain  limits,  of  reducing  this  error  to  zero.  He 
first  located  this  plane  in  the  center  of  the  bar,  as  was  done  in  the 

*  See  Report  of  Professor  Ililgard,  U.  S.  Coast  and  Geodetic  Survey,  reprinted,  pp.  24-27. 


119 

case  of  the  Imperial  Yard,  but  after  further  investigation,  he 
concluded  that  it  was  not  quite  one-third  the  thickness  of  the  bar 
below  the  graduated  surface. 

He  found  that  the  errors  from  the  effect  of  flexure  depended 
upon  the  thickness  of  the  bars  as  compared  with  each  other,  and 
when  resting  upon  a  surface  which  is  not  plane  (Phil.  Trans. 
1830.)  He  also  found  that  this  error  far  exceeds  that  which 
would  arise  from  the  difference  of  the  length  of  the  arc  and  its 
chord  under  the  same  circumstances ;  so  much  so,  that  in  a  bar 
an  inch  thick,  with  the  versed  sine,  that  is,  the  distance  at  the 
center  of  the  bar  from  the  horizontal  plane  joining  the  two  ends 
to  the  curved  surface,  equal  to  one  hundredth  of  an  inch,  the 
sum  of  the  errors  would  be  nearly  one  thousandth  of  an  inch  in 
the  length  of  a  standard  yard.  To  overcome  the  objection  of  a 
variable  result  at  every  position  of  a  standard  bar,  the  number  of 
supports  for  it  has  been  carefully  determined,  and  in  the  case  of- 
the  Imperial  Bronze  1,  the  number  of  these  supports  is  eight, 
and  having  been  decided  by  Mr.  Baily  to  be  necessary,  this  was 
adopted  for  the  national  standards.  The  distance  between  the 
supports  is  about  4£  inches. 

Sir  George  Airy  gave  a  formula  for  determining  the  distance 
between  the  supports  for  any  standard  bar,  in  order  to  neutralize 
the  effect  of  flexure.  It  is 

Length  of  the  bar, 


"  n  "  being  the  number  of  supports. 

In  the  bar  we  now  have  before  us,  the  condition  under  which 
it  was  transferred,  and  also  when  investigated,  was  when  resting 
upon  two  supports,  and  using  the  formula  just  given,  the  distance 
between  them  is  about  22  inches,  the  total  length  being  38 
inches.  You  will  notice  it  places  the  supports  a  little  Jess  than 
one  quarter  the  length  of  the  bar,  measured  from  each  end.  This 
gives  the  surface  a  certain  permanence  or  equilibrium  of  position 
when  resting  upon  any  level  surface,  whether  a  true  plane  or  not, 
and  if  used  thus  under  the  same  conditions  of  support  and  tem- 
perature, the  distance  between  the  defining  lines  remains  the 
same.  If  we  move  the  supports  each  nearer  the  ends,  say  an 
inch  and  a  half,  the  surface  changes  slightly,  and  the  result 


120 

is   to    bring  the   lines  at  each  end  nearer  together,  as  we  have 
just  mentioned. 

According  to  the  Report  of  Professor  J.  E.  Hilgard,  Chief 
U.  S.  Coast  and  Geodetic  Survey,  in  charge  of  Verification  of 
Standards,  1880,  Bronze  No.  1  is  kept  at  a  very  uniform  tem- 
perature within  the  walls  of  the  Houses  of  Parliament,  while 
Bronze  No.  6,  which  is  the  accessible  national  standard,  is  pre- 
served in  the  Strong  Room  of  the  Old  Treasury,  now  No.  7,  Old 
Palace  Yard.  There  is  not  now  any  perceptible  difference 
in  the  lengths  of  these  two  Standards. 

The  Imperial  Yard  is  in  charge  of  Dr.  H.  J.  Chancy,  his 
official  position  being  Warden  of  the  Standards. 

In  order  to  secure,  as  far  as  possible,  accurate  duplicates  of  the 
new  standard,  four  Parliamentary  copies  were  constructed^  one 
of  which  is  kept  in  the  Royal  Mint,  one  is  in  charge  of  the 
Royal  Society,  one  is  preserved  in  the  new  Westminster  Palace, 
and  the  other  is  kept  at  the  Royal  Observatory  at  Greenwich. 

There  were  also  40  copies  made  of  Baily's  metal  for  distribu- 
tion among  the  different  governments.  Only  two  of  these  40  bars 
are  exactly  standard  at  62°  Fahr.,  these  are,  Bronze  19,  and 
Bronze  28.  Both  are  kept  at  the  Royal  Observatory  for  refer- 
ence, as  representing  the  national  'standards.  All  the  other 
copies  have  a  certain  relation  to  Bronze  1,  and  instead  of  giving 
this  relation,  the  temperature  at  which  they  are  standard  is 
established  for  each. 

The  standards  prepared  by  Mr.  Sheepshanks  were  legalized  by 
Act  of  Parliament,  June  30,  1855,  and  in  1856  Bronze  11,  one  of 
the  40  copies  made  of  Baily's  metal,  was  presented  to  the  United 
States  Government  by  the  British  Board  of  Trade,  and  was  then 
standard  at  61°. 79  Fahr.  This  bar  is  deposited  in  the  office  of 
the  United  States  Coast  Survey  at  Washington.  It  has  since 
been  found  that  Bronze  No.  11  is  shorter  than  Bronze  No.  1  by 
0.000088  of  an  inch  at  62°  Fahr.  from  comparisons  made  by 
Professor  J.  E.  Hilgard,  who,  in  1878,  compared  it  directly  with 
the  Imperial  Yard  at  the  Standards  Office  in  London.  Conse- 
quently, to  be  standard,  it  must  be  considered  so  at  62°. 25  Fahr.* 

Previous  to  1856,  the  distance  between  the  27th  and  63d  line 

*  See  Methods  and  Remits,  American  Standards  of  Length,,  U.  S.  Coast  and  Geodetic  Survey, 
Appendix  No.  12— Report  for  1877,  pages  33  and  35. 


121 

of  the  brass  scale  of  82  inches,  made  by  Trotighton,*  was  taken 
as  standard,  though  never  having  been  legalized  by  Act  of  Con- 
gress it  had  an  indirect  authority,  as  it  was  adopted  by  the  Treas- 
ury Department  in  1832,  on  the  recommendation  of  Mr.  Hassler 
(Weights  and  Measures  Eeport,  Washington,  1857),  and  copies 
of  it  were  made  for  distribution  among  the  different  States,  under 
the  charge  of  Mr.  Joseph  Saxton. 

The  fact  is  noticeable  that  all  the  copies  of  the  Imperial  Yard 
are  made  of  the  same  material  as  that  of  the  original  Bronze  1. 
This  is  no  doubt  owing  to  the  greater  uniformity  obtained  in  the 
coefficient  of  expansion  for  each  standard  bar,  admitting  of  com- 
parisons at  any  temperature.  Comparisons  otherwise  would  not 
be  possible,  except  for  bars  of  other  metals  whose  coefficient  or 
rate  of  change  for  each  degree  of  temperature  was  definitely 
known,  and  even  with  this  knowledge  it  would  present  an  exceed- 
ingly nice  problem. 

To  illustrate  this  in  a  few  words.  If  a  steel  bar  or  a  platinum 
standard  be  compared  with  one  made  of  brass  or  Baily's  metal, 
and  each  were  standard  only  at  62°,  if  we  should  compare  them 
at  72°  we  would  find  them  not  alike  in  length,  because  brass 
expands  more  for  each  degree  of  rise  of  temperature  than  does 
the  steel  or  the  platinum ;  the  difference  would  be  greater  in  the 
comparison  of  platinum  with  the  brass  standard,  as  steel  and 
brass  have  a  coefficient  more  nearly  alike. 

Let  us  now  briefly  refer  to  what  has  been  done  to  fix  perma- 
nently the  metric  standard  of  length.  The  metric  system  is 
represented  in  Great  Britain  by  two  bars  made  of  platinum,  one 
being  a  line-measure,  and  the  other  an  end-measure  standard. 

These  bars  are  of  the  following  dimensions : 

(  Length,      41.000  inches. 
Line  Meter,      .     .      1  Breadth,       1.000       " 
(  Thickness,   0.211       " 

Length,      39.37-1-      " 

End  Meter,      .     .      J  Breadth,       1.000       " 
(  Thickness,  0.287       " 

The  defining  lines  nearly  traverse  the  face  of  the  bar  for  the 
line  meter,  and  arrows  arbitrarily  placed,  indicate  the  position  on 
the  lines  where  measurements  are  to  be  made. 

*See  House  Doc.  No.  299,  XXII  Congress,  first  session,  and  also  Am.  Phil.  Society  Trans., 
vol.  2,  new  series. 


122 

The  line  meter  lias  the  words  "  Royal  Society,  45  "  engraved 
on  the  under  side.  The  end  meter,  being  made  of  so  soft  a 
material  as  platinum,  is  not  at  present  in  a  condition  to  use  as  a 
standard  for  very  accurate  work,  the  edges  of  the  end  surface 
being  indented  and  other  signs  of  change  in  the  surface  being 
visible.  The  end  meter  has  the  words,  "  Metre  a  Bouts " 
engraved  on  one  side,  and  "  Fortin  a  Paris,  Royal  Society,  44," 
on  the  other.  These  bars,  together  with  the  original  standard 
prepared  by  Hassler  in  1832,  are  the  only  recognized  standards 
which  have  been  compared  directly  with  -  the  "Metre  des  Arch- 
ives," as  the  French  standard  is  called. 

The  Meter  of  the  Archives,  as  already  stated,  is  made  of  plati- 
num and  iridium,  the  dimensions  being  about  the  same  as  the 
metric  standard  in  London,  and  this  bar  was  made  a  legalized 
standard  after  all  attempts  to  make  it  conform  to  a  natural  unit 
were  abandoned.  It  is  standard  only  at  0°  Centigrade,  or 
32°  Fahrenheit.  Thus  we  see,  that  after  all,  the  actual  use  of  a 
natural  unit  for  creating  and  reproducing  a  standard  of  length 
was  not  realized ;  and  standards,  made  standard  by  law,  were 
really  the  final  result. 

It  has  been  said  that  "  a  mystery  is  a  truth  hid  behind  some 
other  truth,  and  about  which  the  latter  throws  a  veil,"  and  it 
would  seem  as  if  this  definition  might  apply  to  the  great  difficul- 
ties met  with  in  the  attempts  to  obtain  a  standard  of  length  from 
natural  laws  and  natural  conditions,  using  the  grand  truths 
which  are  known  and  accepted,  but  which  seem  to  throw  just 
enough  uncertainty  around  the  truth  sought  as  to  make  the 
results  doubtful  for  the  purposes  for  which  they  are  intended. 
Truth  is  exacting,  it  allows  for  no  "  errors  of  observation  "  or  of 
<; personal  equation,"  and  in  no  other  kind  of  investigation  does 
this  requirement  seem  more  difficult  to  be  fulfilled,  as  so  many 
"  variables  "  —  to  use  a  mathematical  term  —  enter  into  the 
problem ;  variations  of  temperature,  internal  strain  due  to  posi- 
tion of  the  bar;  errors  of  curvature;  errors  of  observation  in 
using  optical  instruments ;  differences  in  material  or  of  density, 
thus  affecting  the  rate  of  expansion  or  contraction,  and  a  score  of 
other  variables,  all  tending  to  make  the  problem  a  complicated 
one.  We  cannot  fail  to  realize  —  at  least  partially  —  the  won- 
derful skill  and  patience  necessary  to  conduct  the  experiments 


123 

which  gave  us,  as  English  speaking  people,  the  Standard 
Imperial  Yard,  which  50  years  ago  were  engaging  the  attention 
of  some  of  the  greatest  minds  the  world  has  ever  known. 

o 

There  is  still  another  natural  unit  which  has  been  proposed  as  a 
standard  of  length.  This  is  the  length  of  a  wave  of  monochro- 
matic or  single  color  light. 

We  have  all  seen  the  beautiful  colors  so  wonderfully  arranged 
in  the  thin  film  of  a  soap  bubble.  These  colors  are  caused  by 
what  is  termed  "  interference."  To  briefly  explain  this  kind  of 
interference,  we  should  know  that  light  is  made  up  of  seven  dis- 
tinct colored  rays,  which  blended  together  produce  clear  color- 
less light.  Each  of  these  separate  rays  has  an  undulatory 
or  wave  motion  through  space,  and  the  length  of  a  wave,  or  the 
distance  from  the  crest  of  one  wave  to  the  top  of  the  next,  is  dif- 
ferent for  each  as  compared  with  one  of  unlike  color,  but  con- 
stant for  its  own  ;  that  of  the  green  ray,  for  instance,  being  com- 
puted as  being  about  3-ovro  o  of  an  inch  from  crest  to  crest. 

When  light  is  reflected  from  the  two  surfaces  of  the  thin  film 
of  a  soap  bubble  to  the  eye,  a  portion  of  it  must  evidently  travel 
a  distance  twice  the  thickness  of  the  thin  film  of  the  bubble,  as 
part  is  reflected  from  the  outer  and  part  from  the  inner  surface  of 
the  film.  The  particular  ray  which  must  thus  travel  farther, 
loses  a  half  of  a  wave  length  in  the  reflection,  so  that  when 
these  two  portions  of  the  reflected  light  come  into  the  same  path 
again,  there  is  more  or  less  interference,  and  if  the  retardation 
lias  been  such  that  the  wave  crest  of  one  falls  into  the  trough  of 
the  other,  they  completely  neutralize  each  other,  and  the  corre- 
sponding color  rays  are  destroyed.  Without  attempting  the 
mathematical  discussion  of  this  subject,  we  know  that  when  this 
relation  happens  more  or  less  coincident,  the  rays  are  either 
deadened  or  are  so  blended  that  they  form  the  beautiful  rings  or 
bands  so  often  noticed.  As  the  film  of  the  bubble  changes  in 
thickness,  these  colors  are  rearranged,  as  different  sets  of  color 
rays  or  waves  are  deadened  and  as  different  colors  disappear  from 
the  reflected  light. 

The  adoption  of  this  unit,  no  doubt,  could  be  relied  upon  to 
produce  a  standard  within  certain  small  limits,  but  the  addition 
or  multiplication  of  such  minute  units  for  the  purpose  of  obtain- 
ing a  practical  standard  of  length  might  introduce  errors  in  the 


124 

total,  greater  than  would  be  likely  to  result  from  either  of  the 
methods  already  mentioned. 

The  use  made  of  this  unit  seems  to  confirm  the  theories  in 
regard  to  the  limit  of  divisibility  of  matter,  and  these  same  soap 
bubbles  which  are  such  a  delight  to  children  —  and  we  might 
include  some  of  the  older  people  as  well  —  have  shown  a  way  in 
which  to  estimate,  in  a  purely  scientific  discussion,  the  dimen- 
sions, approximately,  of  a  molecule,  a  form  of  matter  so  minute 
that  the  smallest  object  visible  under  the  most  powerful  micro- 
scope is  made  up  of  countless  numbers  of  them. 

It  has  been  demonstrated  that  the  mechanical  energy  required 
to  pull  apart  the  molecules  of  water  in  forming  steam,  is  no 
greater,  according  to  the  theory  of  capillary  action,  than  is 
required  to  reduce  the  thickness  of  a  film  of  water  to  the 
3Tro-,woYoiro  of  an  inch ;  a  force  quite  large  when  compared  with 
the  small  amount  of  water  which  we  are  considering.  The 
measurement  of  this  minute  thickness  is  based  upon  the  varying 
colors  exhibited  in  the  soap  bubble,  using  the  length  of  any  given 
wave.  Probably  before  this  extreme  tenuity  could  be  attained, 
there  would  remain  only  a  single  layer  of  molecules  held  together 
by  their  mutual  attraction,  giving  as  the  estimated  average  diame- 
ter of  a  molecule  the  ^oyoio^orir  °^  atl  incn>  a  dimension  so  in- 
finitely minute  as  to  be  quite  beyond  our  ability  to  realize. 

Sir  William  Thomson,  from  a  comparison  of  these  phenomena, 
has  estimated  the  limits  of  range  or  size  of  these  minute  mole- 
cules to  be  between  ^S^TTOOYO o o"  and  s\Tnru,i?F?r,-<nn5-  of  an  inch,  and 
in  order  to  give  some  conception  of  the  "  coarse-grainedness,"  as 
he  calls  it,  thus  indicated,  he  has  said,  "  that  if  we  conceive  a 
sphere  of  water  as  large  as  a  pea,  magnified  to  the  size  of  the 
earth,  each  molecule  being  magnified  in  the  same  proportion,  the 
magnified  structure  would  be  coarser  grained  than  a  heap  of 
small  lead  shot,  but  less  coarse  grained  than  a  heap  of  cricket 
balls." 

We  can  thus  faintly  attempt  to  grasp  the  idea  of  the  infinite 
divisibility  of  matter,  and  to  realize  more  fully  that  the  science 
of  exact  measurement  of  length  must  stop  far  short  of  this  limit, 
as  it  does  far  short  of  the  limit  of  infinite  extension. 

We  have  now  seen  how  difficult  has  been  the  work  of  obtain- 
ing a  standard  for  final  reference,  and  as  it  must  certainly  be  sup- 


125 

posed  to  remain  an  invariable  or  fixed  length  after  having  been 
once  established,  great  care  must  be  taken  to  preserve  this  stand- 
ard from  injury,  which  may  be  caused  either  by  wear  or  oxida- 
tion, or  by  change  of  form  caused  by  flexure  or  internal  strain. 

The  materials  available  for  standards  of  length,  taken  in  the 
order  of  the  rate  of  their  expansion  under  the  same  conditions  of 
temperature,  are  wood,  glass,  platinum,  gold,  silver,  iron,  brass, 
and  copper.  Wood  may  be  rejected  at  once  for  our  purpose, 
though  it  does  very  well  for  yard-sticks  and  pocket-rules  for 
everyday  use.  Glass  has  been  and  is  now  used  in  certain  cases, 
though  its  great  brittleness  restricts  its  use,  and  the  changes 
going  on  within  its  structure  are  now  the  subject  of  rigid  investi- 
gation by  Professor  Rogers,  requiring  time  to  prove  its  value  as 
a  material  for  standards. 

Platinum,  alloyed  with  about  10  per  cent,  of  iridium,  as  you 
will  remember,  is  used  for  the  Meter  of  the  Archives,  and  also 
for  the  bars  representing  the  line  and  end  meter  standards  in 
Great  Britain,  to  which  reference  has  already  been  made. 

Gold  and  silver  may  be  said  to  be  excluded  for  various  reasons, 
that  of  cost  in  the  case  of  gold,  and  its  extreme  softness,  and  sil- 
ver, because  of  its  great  affinity  for  sulphur,  which  is  always 
present  in  the  atmosphere  of  cities,  forming  the  dark  sulphide 
which  would  soon  ruin  it  for  use  as  a  standard.  There  is,  how- 
ever, a  silver  centimeter  scale,  ruled  by  Brunner  of  Paris,  sub- 
divided into  100  parts,  in  the  office  of  the  Coast  Survey  at 
Washington. 

Iron  bars  were  used  by  the  French  Commission,  four  standards 
being  made  of  this  material,  with  polished  ends.  From  one  of 
them  was  constructed  the  platinum  Meter  of  the  Archives.  One 
of  these  bars,  the  only  one  known  to  be  in  existence,  bearing  the 
stamp  of  the  Commission,  is  now  in  the  possession  of  the  United 
States  Coast  Survey  at  Washington. 

The  Russian  standard  of  length,  used  for  geodetic  surveys,  was 
constructed  of  iron,  using  conical  pieces  of  tempered  steel  in  each 
end.  This  bar  has  a  length  of  seven  feet. 

We  have  already  noticed  how  largely  brass,  or  Baily's  metal, 
has  been  used  for  the  standard  yard  and  for  the  numerous  copies 
made  of  it.  There  remains  only  a  brief  mention  of  standards 
made  of  copper.  M.  Tresca,  Acting  Director  of  the  Conserva- 


126 

tory  of  Paris,  constructed  a  copper  line  meter  of  a  form  wliich  lie 
proposed.  The  bar  is  X  shaped,  very  light  and  strong,  and  lias 
the  lines  ruled  on  a  plane  midway  between  the  top  and  bottom 
edges. 

The  method  adopted  at  the  Conservatory  in  Paris  for  compar- 
ing the  platinum  line  meter  bar  with  the  end  "  Metre  des  Arch- 
ives" is  the  use  of  a  plate  having  the  same  thickness  as  the 
meter,  to  which  is  attached  a  thin  piece  of  platinum  terminating 
in  a  sharp  point.  As  a  statute  law  forbids  contact  of  any  kind 
whatever  in  the  use  of  this  platinum  end  meter,  the  reflection  of 
this  sharp  point  upon  the  surface  of  the  end  of  the  standard 
gives  the  means  of  observing  the  instant  of  contact  without  con- 
tact being  actually  made.  It  is  the  opinion  of  M.  Tresca  that 
the  error  can  be  in  this  way  reduced  below  1  mikron  (==  .001mm, 
or  about  ^3-,-J-oiy  of  an  inch),  in  the  transfer  to  line-measure. 

After  having  thus  briefly  considered  the  subject  of  the  "  evolu- 
tion" of  a  standard,  and  the  conditions  under  which  it  must  con- 
tinue in  order  to  be  worthy  of  being  called  a  standard,  we  will 
now  attempt  to  show  some  of  the  methods  adopted  for  compar- 
ing these  yard  or  meter  bars,  and  explain  some  of  the  principles 
upon  which  the  accuracy  of  the  comparison  depends. 

We  have  already  partly  described  the  way  in  which  the  end 
meter  is  compared  or  transferred  to  a  line-measure  by  the  reflec- 
tion of  a  fine  point  of  platinum,  without  actually  touching  the 
ends  of  the  standard  bar.  We  may  now  notice  how  two  stand- 
ard end-measure  bars  may  be  compared,  using  a  method  by 
wThich  the  diiferences,  if  any,  are  greatly  magnified,  and  are  thus 
more  readily  determined. 

A  most  ingenious  application  of  the  laws  of  the  reflection  of 
light  was  made  by  Joseph  Saxton  for  comparison  of  end-measure 
bars,  and  for  which,  in  recognition  of  its  value  to  science,  he  was 
in  1837,  awarded  the  John  Scott  Legacy  Medal,  his  invention 
being  the  Reflecting  Comparator.  The  principles  of  its  construc- 
tion depend  upon  the  magnified  distance  traversed  by  a  reflected 
ray  of  light  caused  by  the  rotation  of  a  mirror  placed  vertically 
and  delicately  pivoted,  the  spindle  of  the  mirror  being  connected 
with  a  sliding  bar  by  a  fine  watch  fusee  chain  wound  around  the 
barrel  of  the  mirror  spindle.  At  the  end  of  the  sliding  bar  to 
which  this  chain  is  attached,  contact  is  made  with  the  end  of  the 


127 

standard  to  be  compared,  the  other  end  of  the  standard  being 
firmly  abutted  against  an  immovable  "  stop." 

By  first  placing  the  standard  bar  in  position,  care  being  taken 
to  have  the  bar  supported,  as  you  will  remember,  at  the  "  neutral 
points,"  and  exactly  in  line  so  that  the  centers  of  the  opposite 
ends  of  the  standards -are  against  the  contact  surfaces  of  both  the 
stationary  and  the  sliding  stops —  and  wrhich,  by  the  way,  is  one 
of  the  most  difficult  features  of  the  experiment  — a  ray  of  light 
is  brought  to  bear  upon  the  mirror,  and  the  reflection  of  a  circu- 
lar scale  is  observed  through  a  small  telescope,  mounted  just  above 
this  divided  arc.  This  circular  scale  may  be  placed  at  any  con- 
venient distance  from  the  mirror,  say  15  or  20  feet. 

It  is  evident  that  a  very  slight  motion  of  the  sliding  bar,  6r,  in 
the  figure  shown  upon  the  screen,  (Fig.  13,)  will  cause  a  ray  of 
light,  reflected  from  the  mirror,  J/,  to  which  its  motion  is 


Top, 


FIG.  13. 

imparted  through  the  small  chain  and  drum,  to  move  with  a 
much  greater  velocity  at  the  distance  of  the  large  circular  scale, 
R  S,  and  as  the  angle  of  incidence  is  equal  to  the  angle  of  reflec- 
tion, a  motion  of  the  mirror  through  an  arc  of  5  degrees  would 
cause  a  motion  of  the  reflected  ray  of  10  degrees,  as  may  be  more 
readily  understood  by  taking  the  geometrical  proof  in  illustration. 


128 


If  a  polished  surface  is  so  placed  that  the  light  strikes  it 
"  squarely,"  or,  in  other  words,  at  no  angle  whatever,  it  will  evi- 
dently be  reflected  directly  back  to  its  source.  Now,  suppose  it 
is  rotated  into  such  a  position  as  indicated  in  the  accompanying 
figure,  (Fig.  13a,)  which  is  just  45  degrees  as  compared  with  its 
original  inclination,  the  light  still  coining  from  the  same  direction  ; 


FIG.  13a. 

it  now  strikes  it  at  an  angle  of  45  degrees,  and  as  light  is  always 
reflected  at  the  same  angle  as  that  at  which  it  is  received  upon 
a  polished  surface,  its  new  path  will  be  again  45  degrees  from 
the  plane  of  the  mirror;  but,  as  you  will  see,  it  is  twice  45 
degrees  with  respect  to  its  incident  path,  and  is  thus  actually  re- 
flected at  an  angle  of  90  degrees. 

We  can  readily  see  how  extremely  delicate  or  sensitive  to  the 
slightest  change  of  position  this  reflected  ray  becomes.  As  light 
may  be  said  to  have  no  weight,  and  consequently  no  inertia  or 
momentum,  it  will  quickly  and  certainly  indicate  the  slightest 


129 

change  in  length  of  a  standard  end-measure  bar,  if  investigated 
in  this  way. 

By  calculating  the  length  of  the  relative  "  lever  arms  "  we  can 
easily  determine  the  magnifying  capacity  of  such  an  instrument 
of  precision.  For  instance,  supposing  the  drum  on  the  spindle 
to  which  the  rotating  mirror  is  attached  is  one-quarter  of  an  inch 
in  diameter,  and  that  the  length  of  the  radius  of  the  large  circular 
scale  is  20  feet,  we  have,  using  the  double  angle  in  this  relation, 
the  distance  moved  by  the  sliding  bar  touching  the  standard,  as 
compared  with  the  arc  passed  over  by  the  reflected  ray  at  the  dis- 
tance of  20  feet  from  the  mirror,  and  reducing  to  the  same  unit, 
as  £  x  is  x  -A  —  Wro  is  to  1,  or  as  1  is  to  3,840 ;  hence  a  motion, 
or  variation  of  one  thousandth  of  an  inch  at  the  point  of  contact 
would  be  represented  as  3.84  inches  on  the  scale. 

By  placing  a  metallic  bar  in  a  closed  tube,  the  ends  only 
projecting  through  this  tube,  and  filling  the  tube  with  ice  water, 
then  with  water  of  a  known  higher  temperature,  and  com- 
paring the  lengths  of  the  same  bar  under  these  varying  condi- 
tions, the  amount  of  expansion  for  each  degree  can  be  deter- 
mined; this  will  give  us  what  is  called  the  coefficient  of  expan- 
sion, to  which  reference  has  already  been  made. 

The  comparator  in  use  by  the  United  States  Coast  Survey  at 
Washington,  designated  as  the  Saxton  Yard  Dividing  Compara- 
tor, is  one  designed  by  Mr.  Saxton  while  in  charge  of  the  con- 
struction of  standard  balances,  weights,  and  measures  of  length,.. 
to  be  presented  to  the  different  States,  to  insure  uniformity 
throughout  the  country. 

A  short  description  of  this  comparator  may  be  quoted  from  a- 
paper  read  by  Professor  W.  A.  Eogers  before  the  American. 
Academy  of  Arts  and  Sciences,  April  14,  1880,  "  On  the  Present 
State  of  the  Question  of  Standards  of  Length,"  and  from  which, 
also,  much  that  is  of  interest  in  regard  to  our  subject  matter  for 
this  evening  has  been  obtained.  Any  one  wishing  to  pursue  the 
subject  further,  the  paper  entire,  and  the  references  contained  at 
the  end  will  be  of  great  assistance. 

"  The  Saxton  Comparator  consists  of  a  brass  bed-plate,  having 
Y-shaped  ways  running  the  entire  length.  A  slide  carrying  a 
microscope  slides  freely  over  these  ways. 

"  A  series  of  brass  posts  form  a  part  of  this  bed,  through  which 


130 

pass  steel  screws,  having  conical  ends,  which  have  been  tempered 
and  polished.  There  are  stops  for  the  yard  and  for  its  subdivi- 
sion into  feet,  and  of  one  foot  into  inches.  There  are  also  stops 
for  the  meter  and  for  its  subdivision  into  decimeters,  and  of  one 
decimeter  into  centimeters.  .  .  .  The  end  stops  for  the  yard 
and  for  the  meter  were,  many  years  ago,  set  to  correspond  with 
"  Bronze  No.  11,"  at  58°  nearly,  for  the  yard,  and  with  the  iron 
meter  at  68°  nearly.  .  .  .  The  standards  which  have  been 
distributed  since  1856  have  been  transferred  from  these  distances 
at  the  temperatures  at  which  they  are  standard. 

"  The  yard  in  actual  use  at  the  Bureau  of  Weights  and  Meas- 
ures, therefore,  may  be  defined  to  be  the  distance  between  two 
steel  stops  attached  to  the  bed  of  the  Saxton  Comparator  which 
corresponds  to  the  length  of  Bronze  No.  11,  at  58°  nearly,  and  the 
meter  may  be  defined  to  be  the  distance  between  two  steel  stops 
of  the  Saxton  Comparator  which  corresponds  to  the  length  of  the 
iron  meter  corrected  for  the  differences  between  its  length  at  32° 
and  at  68°,  nearly.  Recent  comparisons  indicate  that  these  tem- 
peratures should  be  diminished,  by  a  trifling  amount,  for  the 
present  distances  between  the  stops  both  for  the  yard  and  for  the 
meter." 

Engravings  representing  the  Saxton  Yard  Dividing  Compara- 
tor *  and  also  the  Saxton  Reflecting  Comparator  which  are  here 
shown  (Fig.  13,  p.  127),  were  obtained  through  the  kindness  of 
Professor  J.  E.  Hilgard, Chief  U.S. Coast  Survey, by  whom  every 
facility  was  afforded  me  for  examining  the  methods  of  comparison. 
The  courtesy  of  Mr.  Blair,  assistant  in  charge,  has  aided  me 
greatly  in  thus  being  able  to  illustrate  the  instruments  now  in 
use  at  the  office  of  the  Coast  Survey. 

Another  form  of  a  comparator,  which  has  proved  to  be  success- 
ful in  the  "  use  of  the  means  for  the  end  sought,"  in  the  compari- 
son and  investigation  of  standards  of  length,  is  that  known  as 
the  Rogers-Bond  Universal  Comparator  (Fig.  15),  which  was  con- 
structed from  plans  proposed  by  Professor  Rogers,  by  The  Pratt 
&  Whitney  Company  of  Hartford,  Conn.,  for  their  use  in  practi- 
cally establishing  standard  gauge  dimensions.  A  duplicate  com- 
parator of  this  form  was  also  made  by  the  Company  for  Professor 
Rogers  for  his  professional  work  at  Cambridge,  and  for  the  trans- 

•  Shown  on  the  screen  only. 


131 

fer  and  comparison  of  line-measure  standards  used  by  The  Pratt 
&  Whitney  Company  as  the  basis  of  these  standard  gauges. 

The  comparator  at  Cambridge*  is  also  used  by  Professor  Rogers 
in  determining  the  coefficients  of  expansion  of  the  various  mate- 
rials used  in  the  construction  of  standard  yard  and  meter  bars, 
arid  also  for  obtaining  the  relation  between  the  length  of  the  Im- 
perial Yard  and  the  "  Metre  des  Archives."  The  solution  of 
this  latter  interesting  and  difficult  problem  is  fully  given  in  a 
Memoir  by  Professor  Rogers,  presented  May  9,  1883,  before  the 
American  Academy  of  Arts  and  Sciences,  entitled  "  Studies  in 
Metrology,"  to  which  reference  may  be  had.f 

The  special  features  of  the  Universal  Comparator  are,  as  its 
name  implies,  the  variety  of  the  methods  employed  and  the 
range  of  work  that  can  be  done  in  comparing  standards;  each 
independent  method,  when  carefully  carried  out,  producing  simi- 
lar results  which  serve  to  check  or  prove  the  comparisons.  It 
includes  a  method  for  investigating  the  subdivisions  of  the  stand- 
ard by  comparing  each  part  of  the  total  length  with  a  constant 
or  invariable  quantity  or  distance. 

By  the  aid  of  the  diagram  of  the  plan  and  elevation  of  this 
form  of  comparator,  the  aim  being  to  exhibit  principles  rather 
than  a  picture  of  the  instrument,  we  may  be  able  to  describe  in  a 
few  words  the  main  features  of  its  construction.  (Fig.  14-,  p.  132.^ 

A  heavy  cast  iron  base  J.,  is  mounted  upon  stone  capped  brick 
piers,  giving  a  permanent  foundation  to  the  apparatus.  Upon 
this  base,  and  reaching  from  end  to  end.  are  two  heavy  steel 
tubes,  B  and  (?,  three  inches  in  diameter,  ground  perfectly 
straight,  and  being  "true"  when  placed  in  the  centers  of  a  lathe, 
the  object  being  to  get  a  straight-line  motion  of  the  microscope 
plate  D,  which  slides  freely  on  these  true  cylinders. 

Flexure  of  these  cylindrical  guides  is  overcome  by  lever  sup- 
ports at  the  neutral  points  n  and  n1.  Fitted  closely  to  these 
guides,  and  outside  of  the  range  of  motion  of  the  microscope 
plate  D  are  two  stops,  E  and  F,  one  at  each  end,  as  shown  in  the 
figure.  These  stops  are  arranged  to  be  adjusted  at  any  desired 
position  along  the  guides,  and  are  securely  held  by  clamping  on 
the  under  side  by  the  handles  G  and  H. 

*  Since  transferred  to  the  Johns  Hopkins  University,  Baltimore,  Md. 
t  See  Professor  Rogers'  Report,  page  19. 


132 


133 


These  stops  are  each  provided  with  a  pair  of  electro-magnets, 
/and*/,  the  poles  of  which  do  not  quite  come  in  contact  with  the 
armature  seen  at  either  end  of  the  microscope  plate.  Contact  is 
made  at  K and  L,  which  are  hardened  steel  surfaces,  tempered 
and  polished,  and  placed  as  nearly  as  possible  in  the  center  of 
mass  of  the  plate  and  of  the  stops. 

The  magnets  are  intended  to  overcome  the  unequal  pressure 
due  to  ordinary  contact,  a  rack  and  pinion  being  used  to  move 
the  plate.  The  magnets  are  used  to  lock  the  microscope  plate  at 
each  end  of  its  traverse  between  the  stops.  The  use  made  of 
this  sliding  microscope  plate  and  the  stops  we  shall  see 
presently. 


FIG.  15. 

THE  ROGERS-BOND  UNIVERSAL  COMPARATOR. 
(Patented  Dec.  8,  1885). 


134 

Beyond  the  main  base  just  described,  and  supported  also  on  brick 
piers,  is  an  auxiliary  heavy  cast  iron  frame  A7,  which  is  provided 
with  lateral  and  vertical  motion  within  limits  of  zero  and  of  8  and 
10  inches,  respectively,  for  rough  or  approximate  adjustment, 
and  upon  the  top  of  this  frame  are  two  carriages,  0  and  Ol, 
which  slide  from  end  to  end,  a  distance  of  about  40  inches. 
Upon  these  sliding  carriages  are  placed  tables  T and  7",  provided 
with  means  for  minute  adjustment,  for  motion  lengthwise,  side- 
wise,  and  for  leveling,  thus  permitting  the  adjustment  of  a  stand- 
ard yard  bar  quickly,  and  without  the  necessity  of  its  being 
touched  with  the  hands  after  being  placed  upon  the  table  until 
the  work  of  comparison  is  completed.  A  view  of  this  comparator 
in  perspective  is  shown  in  Fig.  15.* 

Before  describing  the  operations  necessary  for  a  series  of  com- 
parisons, it  may  be  well  to  explain  the  peculiar  fitness,  for  pur- 
poses of  this  kind,  of  the  microscopes  M  and  If  used  in  this 
connection. 

The  tubes  are  12  inches  long  and  1J  inches  diameter,  the  eye- 
piece micrometers  ml  and  m  were  made  by  Joseph  Zentmayer, 
of  this  city  (Philadelphia),  whose  skill  as  an  optician  is  too  well 
known  to  require  further  proof  of  their  excellence.  The  object- 
ives were  made  by  the  late  Mr.  R.  B.  Tolles  of  Boston,  and  are 
each  fitted  with  his  illuminating  prism. 

In  order  to  use  a  microscope  upon  lines  ruled  on  polished  sur- 
faces, or  on  any  opaque  material,  some  means  for  obtaining  suffi- 
cient light  must  be  employed  in  order  to  see  them  distinctly, 
without  the  use  of  reflectors,  which  are  often  a  source  of  error  in 
standard  work. 

In  no  other  form  of  objective  does  this  requirement  seem  better 
fulfilled  than  in  that  invented  and  made  by  Mr.  Tolles.  The 
objectives  are  each  fitted  with  a  prism  of  perfectly  clear  glass, 
placed  just  above  the  lower  lens,  one  end  of  the  prism  passing 
through  the  side  of  the  objective.  The  inner  end  of  this  prism 
is  beveled  (Fig.  16),  forming  an  angle  of  the  end  surface  with  re- 
spect to  the  axis  of  the  prism,  such  that  light  is  refracted  perpen- 
dicularly upon  the  surface  of  the  bar,  so  that  lines  less  than  3^* 
of  an  inch  in  width  are  easily  seen  and  separated  with  a  one- 

*For  further  description,  including  caliper  attachment,  see  pages  50-54,  ante,  (Report  of 
committee  on  Standards  and  Gauges). 


135 


incli  objective.  It  may  be  said  to  "carry  its  own  lantern,"  and 
with  light  so  thrown,  just  where  it  is  most  needed,  the  bottom  of 
the  cut  or  furrow  of  a  line  ruled  by  a  diamond  edge,  as  fine  as 
that  just  stated  (W^-Q-O  of  an  inch),  as  well  as  the  edges  of  the  line, 
are  readily  seen. 

This  method  of  illumination  has  proved  invaluable  in  the 
work  of  comparing  line-measure  standards,  and  especially  so  in  the 
case  of  bars  having  the  lines  ruled  on  polished  gold  surfaces  at 
the  bottom  of  wells  sunk  one-half  the  depth  of  the  bar,  these 
wells  being  not  over  one-half  an  inch  in  diameter,  as  in  the  case 
of  Bronze  1,  and  also  of  the  bar  now  before  you.* 

The  first  operation  in  the  use  of  this  form  of  comparator  is  to 
level  the  main  base,  A,  (Fig.  14,)  then  sliding  the  microscope  plate 
D,  from  end  to  end  of  the  steel  tubular  guides,  having  the  micro- 
scope adjusted  so  as  to  be  in  focus  upon  the  surface  of  mercury 
contained  in  a  shallow  trough,  over  which  the  microscope  passes,' 


FIG.  16. 

the  curvature  due  to  flexure  of  the  guides  is  determined,  and  may 
be  compensated  for  by  counter  weights  at  the  neutral  points  of 
support,  n  and  n\ 

In  order  to  test  this  right  line  path  of  the  microscope  plate 
horizontally,  the  method  of  the  "  stops  "  is  employed,  or,  another 
method,  which  is  that  of  tracing  a  fine  line  the  entire  length  of  a 
standard  bar  upon  its  upper  surface,  and  reversing  the  bar,  trac- 
ing another  line  very  near  the  first  and  at  an  equal  distance  apart 
at  each  end  ;  then  if  this  distance  is  uniform  between  the  two  lines 
the  entire  length,  it  is  safe  to  assume  that  the  path  of  the  plate 
is  a  straight  line  horizontally,  and  at  the  middle  the'  amount 

*  See  Prof.  Rogers'  Report,  page  5  (P.  &  W  .). 


186 

of  curvature,  if  any,  and  if  uniform,  is  readily  determined. 
This  method 'is  used  by  Professor  Rogers  with  complete  success. 

The  "  stop  method  "  is  to  compare  a  line-measure  or  an  end- 
measure  bar,  on  each  side  of  the  center  line  of  motion  of  the 
microscope  plate,  using  one  microscope,  and  comparing  this  fixed 
length  with  the  constant  quantity  before  referred  to,  which  is  the 
distance  between  the  stops.  Should  the  path  be  a  curved  one, 
the  distance  between  the  defining  lines  upon  the  bar  will  appear 
greater  on  one  side  than  on  the  other  in  proportion  to  the  amount 
of  curvature  existing.  The  length  of  the  standard,  being  the 
length  of  chords  of  circles  of  different  radii,  seems,  by  comparison 
with  the  stops,  to  be  different  in  length  at  each  position,  caused 
by  the  different  distances  from  the  center  of  curvature, —  about 
18  inches,  in  this  instance  —  over  which  the  microscope  passes 
when  placed  in  these  two  positions.  By  means  of  the  proportion 
of  similar  triangles  thus  formed,  the  lengths  of  the  radii  may  be 
very  accurately  determined.  By  placing  different  standards  on 
one  side  of  the  line  of  the  stops,  they  may  be,  by  being  compared 
with  a  constant  quantity,  compared  also  with  each  other. 

Another  method  for  comparing  two  or  more  standards,  is  to 
place  two  microscopes,  one  on  each  of  two  microscope  plates, 
upon  the  guides,  at  a  distance  determined  by  the  length  of  one 
of  the  standards,  and  by  replacing  this  one  by  a  second,  the  co- 
incidence of  the  lines  in  the  eye-piece  micrometer,  or  their  varia- 
tion, showing  at  once  their  relation.  The  microscopes  may  be 
placed  horizontally  in  this  same  fixed  relation,  using  the  method 
invented  by  J.  Homer  Lane,  and  which  has  been  successfully 
used  in  the  office  of  the  United  States  Coast  Survey  at  Wash- 
ington. 

There  are  five  independent  methods  for  comparing  standards 
of  length  by  the  use  of  this  form  of  Comparator ;  but  we  \vill  not 
dwell  longer  upon  this  part  of  the  subject,  but  pass  to  the  subdi- 
vision of  these  standards  of  length,  which  is  effected  by  the  use  of 
this  same  process — the  microscope  plate  sliding  between  fixed 
stops  —  and  which  serves  to  beautifully  illustrate  one  of  the  fund- 
amental principles  of  science,  that  "  things  equal  to  the  same 
thing  are  equal  to  each  other,"  or,  that  the  relation  of  different 
lengths  each  to  a  constant  distance,  establishes  their  relation 
to  each  other. 


137 

Tin's  is  accomplished  in  the  following  way :  A  yard,  for  in- 
stance, is  to  be  subdivided  into  three  equal  parts,  or  into  three 
'separate  feet.  We  divide  the  whole  length  by  trial  into  three 
parts,  then,  by  setting  the  stops  so  that  the  microscope  plate 
may  move  very  nearly  the  distance  represented  by  the  first  one 
of  the  three  parts,  by  readings  of  the  eye-piece  micrometer  care- 
fully taken  at  each  end  of  the  path  of  motion  of  the  microscope 
and  using  the  finely-ruled  lines  by  which  these  three  parts  are 
defined,  we  obtain  the  length  of  this  subdivision  as  compared 
with  our  constant  quantity;  then,  by  sliding  or  moving  the  bar 
along  under  the  microscope  until  the  second  part  is  in  place,  the 
same  operation  is  again  performed,  and  so  for  the  third,  thus 
determining  the  relation  of  each  with  respect  to  this  temporary 
or  arbitrary  standard ;  then,  by  adding  the  differences  between 
these  separate  parts  and  the  constant  length,  and  taking  the  mean 
or  average  of  these  differences,  from  which  we  subtract  each 
difference,  gives  us  the  correction  to  be  applied  to  each  part,  in 
order  that  it  shall  be  exactly  one-third  the  total  length,  or,  as  in 
case  of  a  yard  bar,  giving  us  exactly  twelve  inches,  or  the  stand- 
ard foot.  The  foot  may  then  be  subdivided  in  the  same  manner 
into  twelve  equal  parts,  establishing  the  standard  inch,  and, 
further,  to  eighths,  sixteenths,  thirty-seconds,  hundredths,  or  even 
to  thousandths  of  an  inch. 

To  illustrate  this  method,  and  to  make  plain  the  reason  why 
these  corrections  so  obtained  are  used,  we  can  suppose  a  case  of 
simply  dividing  a  rod  or  a  string  in  two  parts.  Now  we  know 
that  for  whatever  amount  one  part  is  longer  than  the  other,  one- 
half  of  this  amount  belongs  to  the  shorter  to  make  it  exactly  one- 
half  the  whole  length  of  the  rod  or  string ;  hence  we  have  one- 
half  the  sum,  or  amount,  of  the  difference,  and  subtracting  each 
difference  from  this  half  sum  would  in  one  case  give  us  a  minus 
correction  for  the  longer  part,  and  a  plus  correction  to  be  applied 
to  the  shorter. 

A  series  of  readings  or  "  observations,"  using  the  microscope 
with  the  eye-piece  micrometer,  and  having  the  correctness  of  the 
subdivision  of  a  standard  yard  into  three  parts  to  determine, 
would  be  after  this  form : 


138 


First  Foot. 

R. 

3.98.2 
3.97.8 
3.98.5 

Mean  3.68.5  Mean  3.98.2 

R-L=+29.7 


Third  Foot. 

R. 

3.97.0 
3.97.8 
3.97.7 


Second  Foot. 


L. 

3.57.4 
3.57.5 
3.57.9 

Mean  3.57.6 


R. 
3.87.3 

3.87.7 
386.9 

Mean  3.87.3 
-L  =  +  29.7 


Correction.  2 
4-29.7  +  2.1 
+  29.7  +  2.1  +  4.2 
+  36.0-  4.2  ±  0.0 


Mean  3.61.5  Mean  3.97.5 

R-L  =  +  36.0 


3)95.4 
Mean  31.8 


The  columns  under  "  L "  are  readings  of  the  eye-piece  mi- 
crometer taken  at  the  left  or  initial  end  of  each  foot,  and  under 
"R,"  readings  taken  at  the  right,  "R  —  L"  being  the  difference 
between  the  readings  taken  at  each  end  of  this  subdivision  of  the 
whole  length. 

The  column  under  "  correction  "  shows  the  amount,  in  divisions 
of  the  micrometer,  needed  to  make  each  foot  exactly  one  third 
the  yard  under  investigation.  Under  "  2  "  these  corrections  are 
added  as  a  check  upon  the  accuracy  of  the  work,  a  precaution 
especially  important  in  the  case  of  a  long  column  of  corrections, 
as  when  the  foot  is  subdivided  into  inches,  or  an  inch  into  six- 
teenths or  thirty-seconds. 

We  have  thus  briefly  traced  the  development  of  standards 
of  length  from  some  of  their  rudest  units  to  that  of  the  present 
British  Imperial  yard  and  its  copies,  and  of  the  meter,  and  shown 
how  the  yard  has,  in  one  way  at  least,  been  subdivided  Avithin  a 
limit  of  about  one  hundred-thousandth  of  an  inch  ;  it  remains 
now  to  show  in  what  way  these  accurate  subdivisions  may  be 
successfully  applied  to  every-day  use  for  work  requiring  such 
nicety,  and  in  our  next  lecture  it  is  hoped  that  our  efforts  may 
not  prove  unsuccessful. 


[Reprinted  from  the  Journal  of  THE  FRANKLIN  INSTITUTE,  May,  1884,  (with 
slight  revision  and  additions.)] 


STANDARDS  OF  LENGTH   AS  APPLIED  TO 
GAUGE  DIMENSIONS. 

BY 

GEORGE  M.  BOND. 
[A  lecture  delivered  before  THE  FRANKLIN  INSTITUTE,  February  29,  1884.] 


In  our  lecture  of  last  week  we  attempted  to  show  in  what  way 
Standards  of  Length  may  be  constructed,  and  how  these  stand- 
ards so  constructed  may  be  subdivided  within  very  close  limits 
of  error.  We  will  now  attempt  to  show  in  what  way  these  sub- 
divisions maybe  applied  to  the  requirements  of  modern  machine- 
shop  practice,  and  how  the  gauges  or  implements  used  in  work 
requiring  interchangeability  of  parts  are  made  so  as  to  insure 
this  accuracy. 

Manufactured  articles  have  been  compared  by  Sir  John  Her- 
schell  to  atoms,  on  account  of  their  uniformity.  The  uniformity 
of  manufactured  articles  may  be  traced  to  very  different  motives 
on  the  part  of  the  manufacturer.  In  certain  cases  it  is  less  trou- 
blesome, as  well  as  less  expensive  to  make  a  great  many  articles 
exactly  alike,  than  to  adapt  each  to  its  special  requirements. 
Thus,  shoes  and  the  uniforms  for  soldiers  are  made  in  large 
numbers,  without  any  design  of  adaptation  to  the  requirements 
of  any  one  man.  In  another  class  of  work  the  uniformity  is 
intentional  and  is  designed  to  make  the  manufactured  articles 
more  valuable  owing  to  this  uniformity.  Thus,  for  instance, 
bolts  and  nuts  of  any  particular  size,  if  alike  or  interchangeable, 
may  be  easily  replaced  when  worn  out  or  lost,  saving  an  immense 
amount  of  trouble,  and  especially,  valuable  time,  in  cases  of  repairs 
where  the  stoppage  of  machinery  or  the  delay  of  a  train  of  cars 
would  be  a  matter  of  serious  loss,  not  only  of  time,  but  also  of 
dollars  and  cents. 


140 

In  the  third  class,  not  a  part  only,  but  the  whole  of  the  value 
of  the  object  arises  from  its  exact  conformity  to  a  given  standard. 
Weights  and  measures  belong  to  this  class,  and  the  adoption 
and  use  of  well-adjusted  standards  of  weight  and  measure  in 
any  country  furnishes  the  evidence  of  the  existence  of  a  system 
of  law  that  regulates  the  business  of  the  people,  enjoining  in  all 
measures  a  conformity  to  the  national  standard. 

There  are  thus  three  kinds  of  usefulness  in  manufactured  arti- 
cles: cheapness,  serviceableness,  and  quantitative  accuracy. 
Which  of  these  was  referred  to  by  Sir  John  Herschel,  we  cannot 
say.  It  is  as  likely  the  last  as  the  first,  though  it  would  seem 
more  probable  that  he  meant  to  assert  that  a  number  of  exactly 
similar  things  cannot  be,  each  of  them  eternal  and  self- existent, 
and  must  therefore  have  been  made.  Hence  he  used  the  phrase 
"manufactured  articles"  to  suggest  the  idea  of  their  being  made 
in  great  numbers  (Encycl.  Brit.,  9th  edition,  vol.  3,  p.  49). 

Adam  Smith,  the  founder  in  England  of  the  science  of  polit- 
ical economy,  in  his  most  important  work,  "  The  Inquiry  into 
the  Nature  and  Cause  of  the  Wealth  of  Nations,"  referred  par- 
ticularly to  the  benefits  derived  from  a  systematic  division  of 
labor.  He  showed  by  apt  illustrations  the  wonderful  results  to 
be  attained  by  this  now  well-known  principle,  both  as  regards 
the  quantity  and  the  quality  of  the  product. 

During  the  score  of  years  from  1Y65  to  1785,  when  Adam 
Smith  was  working  out  his  memorable  treatise  just  referred  to, 
the  inventions  which  have  given  us  the  steam  engine  and  the 
loom  were  being  perfected.  While  Adam  Smith  was  lecturing 
in  Glasgow  from  the  chair  of  moral  philosophy,  James  Watt 
was  selling  mathematical  instruments  in  an  obscure  shop  within 
the  precincts  of  the  same  university,  and  was  working  out  his 
inquiry  into  the  practical  methods  of  applying  steam. 

In  a  paper  read  before  the  Institution  of  Mechanical  Engineers, 
in  Birmingham,  Mr.  Edward  A.  Cooper  states  that  in  a  letter 
written  to  a  friend,  Watt  thought  he  had  attained  remarkable 
mechanical  accuracy  when  a  cylinder  he  had  just  bored  was  so 
true  that  he  could  not  get  half  a  crown  between  the  piston  and 
the  cylinder  anywhere ! 

We  must  not  be  surprised  at  this  remark  when  we  consider 
the  materials  he  used  in  making  his  models,  and  the  probable 


141 

state  of  the  art  of  making  machinery  interchangeable  at  the  time 
he  lived.  He  used  tin  cylinders,  and  soldered  the  joints  in  many 
instances.  Often  he  found  it  gave  better  results  to  hammer  them 
rather  than  to  bore  them.  A  block-tin  cylinder,  eighteen  inches 
in  diameter,  one-fourth  of  an  inch  thick,  when  bored  was  found 
to  be  three-eighths  of  an  inch  out  of  true.  He  speaks  of  ham- 
mering it  with  a  mallet  outside,  using  a  round  piece  of  wood  to 
correct  this  defect. 

Eli  Whitney  was  the  first  to  develop  the  principle  of  quantita- 
tive accuracy  by  the  use  of  the  system  of  interchangeable  parts 
in  the  manufacture  of  arms  for  the  United  States  government, 
early  in  the  present  century.  As  an  evidence  of  the  value  of 
this  system,  in  the  year  1822,  Mr.  Calhoun,  then  Secretary  of 
War  of  the  United  States,  admitted  to  Mr.  Whitney  that  the 
government  was  saving  $25,000  per  year  at  the  two  public 
armories  alone,  by  the  use  of  his  improvements.  This  admission, 
the  figures  being  probably  far  below  the  true  facts  of  the  case, 
serves  to  show  that  Mr.  Whitney  deserved  well  of  his  country  in 
this  department  of  her  service.  Mr.  Whitney  was  noted  for  his 
exactness,  his  motto  being,  that  "there  is  nothing  worth  the 
doing  that  is  not  worth  doing  well"  (Am.  Journal  of  Science  and 
Arts,  vol.  21,  January,  1832). 

In  a  paper  read  by  Mr.  Chanute  before  the  American  Society  of 
Civil  Engineers,  at  a  meeting  held  in  Washington,  June  21, 
1882,  on  "Uniformity  in  Kailway  Kolling  Stock,"  he  stated  that 
"  the  average  cost  of  repairs  in  the  shops  of  the  New  York,  Lake 
Erie  &  Western  Railroad,  for  the  five  years  prior  to  1875,  was 
9.17  cents  per  mile  run  by  locomotives,  while  for  the  past  five 
years  it  was\>nly  4.33  cents.  This  represents  a  saving  of  about 
$675,000  a  year.  This  was  after  the  system  had  been  adopted 
by  the  railroad  company  of  making  parts  of  locomotives  in  dupli- 
cate, using  gauges  and  templates  for  this  purpose.  Had  the  rate 
of  cost  of  1871  prevailed  in  1881,  the  expenses  of  locomotive 
maintenance  would  have  been  $790.492  greater  than  they  were. 
The  conclusion  must  not  be  formed,  however,  that  all  the  above 
savings,  or  even  a  major  part  of  them,  have  resulted  alone  from 
the  system  above  mentioned.  Much  of  the  economy  is  doubtless 
due  to  other  reforms  introduced  by  the  management  of  the  road 
about  the  same  time ;  but  a  considerable  part  is  certainly  due  to 


142 

the  adoption  of  rigid  standards  and  of  interchangeable  parts. 
Moreover,  a  very  considerable  number  of  the  old  engines  still 
remain,  with  all  their  imperfections,  so  that  further  benefits  may 
be  expected  to  result  from  the  system  as  it  becomes  extended  in 
the  future." 

In  the  system  upon  which  are  based  the  gauges  produced  by  The 
Pratt  &  Whitney  Company  for  the  purpose  of  establishing  and  main- 
taining this  interchangeability,  the  sizes  are  all  constructed  from  ac- 
curate subdivisions  of  the  British  yard,  fftade  so  carefully  that  end- 
measure  pieces,  representing  any  subdivision  of  a  foot,  and  taking 
any  of  these  sizes  from  a  quarter  of  an  inch  to  four  inches,  varying 
by  sixteenths,  the  sum  or  combination  of  them,  taken  at  random 
and  in  numbers  sufficient  to  constitute  the  length  of  a  foot,  will  be 
found  to  produce  in  the  total  addition,  exactly  the  same  result. 

When  we  consider  that  in  the  experiment  just  mentioned,  the 
variation  of  only  one  thirty-thousandth  of  an  inch  in  each,  if  all 
one  way,  either  plus  or  minus,  would  amount  to  an  error,  in 
some  cases,  of  over  half  a  thousandth  of  an  inch,  and  particularly 
in  the  case  of  one  combination  where  fifteen  or  sixteen  sizes  were 
added,  it  will  be  seen  that  the  error  would  be  very  perceptible  in 
the  test  which  they  would  thus  be  compelled  to  undergo. 

This  severe  practical  test  was  applied  by  the  Committee  on 
Gauges,  of  the  American  Society  of  Mechanical  Engineers,  in 
their  investigation  of  this  system  of  making  standard  gauges,  a 
set  of  these  end-measure  pieces  being  found  to  be  within  the  limit 
of  accuracy  necessary  to  fulfill  this  condition.* 

In  the  production  of  these  end-measures,  it  is  necessary  that 
the  end  surfaces  be  perfectly  parallel.  This  is  a  matter  which  is 
a  simple  operation  as  done  by  The  Pratt  &  Whitney  Company. 


FIG.  17. 

Two  sides  of  a  hardened  end-measure  standard,  such  as  the  one  we 
have  now  before  us  (Fig.  17),  are  made  as  nearly  perfect  planes  as 

*See  Trans.  Am.   Society  Mechanical  Engineers,  1882,  Vol.  iv,  Report  of  Committee  on 
Standards  and  Ganges,  page  26.    (Reprinted,  page  50,  ante.) 


143 

is  possible,  and  at  right  angles  to  each  other.  The  ends  are  then 
made  perpendicular  to  these  two  surfaces,  by  means  of  a  simple 
fixture  which  holds  the  end-measure  vertically  and  clamps  it  in 
the  angle  of  a  movable  block  of  cast  iron  which  slides  freely 
over  the  plane  surface  of  another  block  also  made  of  cast  iron. 
In  the  center  of  this  latter  block  is  a  copper  matrix  having 
diamond  dust  or  washed  emery  imbedded  in  its  upper  surface. 
The  end-measure  is  passed  rapidly  over  this  surface,  and  being 
held  perpendicularly,  its-  highest  points  are  ground  away,  and 
eventually  this  surface  becomes  a  polished  plane.  The  bar  is 
reversed  and  the  same  conditions  are  applied  to  the  other  end ; 
both  ends  being  perpendicular  to  the  same  planes,  are  conse- 
quently parallel  to  each  other. 

These  parallel  surfaces  being  true  planes,  are,  when  brought 
together,  capable  of  sustaining  the  weight  of  either  one  or  the 
other,  or  in  the  case  of  the  two  which  we  have  before  us,  they 
may  be  held  horizontally  and  still  not  separate.  In  a  lecture  be- 
fore the  Royal  Institution,  June  4,  1875,  Dr.  Tyndall  states  that 
experiments  by  Robert  Boyle,  with  plane  surfaces  placed  in  con- 
tact, show  this  clinging  tendency  even  in  a  vacuum ;  and  that 
with  the  surface  plates  he  used,  made  by  Whitworth,  the  force 
necessary  to  pull  them  apart  was  thirty  times  greater  than  that 
due  to  gravity,  showing  a  mutual  attraction  or  actual  cohesion 
of  the  two  surfaces.  This  is  evidently  the  case,  for  we  know 
that  if  the  particles  or  atoms  of  a  piece  of  steel  are  closely 
enough  associated,  they  form  a  solid  mass.  By  making  their 
condition,  artificially,  as  nearly  like  this  as  is  possible,  the  atoms 
are  brought  comparatively  near  each  other,  and  more  or  less  of 
this  cohesive  force  evidently  results. 

Of  course,  in  the  present  case  we  have  apparently  the  weight 
of  the  atmosphere  to  produce  this  result,  but  if  we  consider  how 
small  the  surface  is  on  which  this  pressure  is  acting,  we  must 
admit  that  part  of  this  clinging  tendency  must  result  from  a 
cohesive  force,  for  in  the  case  before  us,  the  surfaces  in  contact  of 
one  of  these  end-measure  pieces  are  each  less  than  a  quarter  of  an 
inch  square,  and  the  weight  of  a  column  of  air,  even  if  there  was 
a  perfect  vacuum  between  the  two  surfaces,  would  be  scarcely 
enough  to  sustain  this  weight,  even  were  the  surfaces  perfect  planes. 

Perhaps  the  most  marked  example  of  interchangeable  work 


144 

resulting  from  a  standard  gauge  system  is  that  shown  in  the 
thread  gauges  which  represent  the  Sellers  or  Franklin  Institute 
system.  This  form,  proposed  by  Mr.  William  Sellers  in  1864,* 
has,  on  account  of  being  adopted  by  the  Government,  been  called 
the  United  States  Standard  thread.  In  order  to  produce  these 
standard  gauges  and  to  be  able  to  guarantee  them  as  being 
standard,  it  was  necessary  first  to  establish  a  standard  inch.  This 
standard  inch  must  be  one  thirty-sixth  part  of  the  British  Impe- 
rial yard,  no  more,  no  less.  Then  having  obtained  this  standard 
inch,  the  subdivisions  of  it  were  to  be  obtained.  So  much  for 
the  size.  Then  in  order  to  establish  an  angle  of  sixty  degrees  for 
the  angle  of  the  thread,  it  was  necessary  to  produce  this  in  a 
practical  way,  in  order  to  furnish  a  gauge  by  which  tools  could 
be  made  that  would  insure  absolute  practical  accuracy.  This 
"  master  triangle,"  designed  by  Mr.  J.  W.  Heyer,  furnishes  the 
means  of  originating  a  triangle  which  shall  be  equi-angular,  and 
consequently  possessing  angles  of  sixty  degrees. 

In  order  to  obtain  accurately  the  width  of  the  flat,  which  is 
one-eighth  of  the  pitch,  for  top  and  bottom  of  the  United  States 
Standard  thread,  it  was  necessary  to  establish  a  model  triangle 
as  a  starting  point,  in  connection  with  this  master  triangle.  This 
model  was,  when  finished,  two  inches  long  on  each  side. 

The  method  used  for  obtaining  a  triangle  having  sides  known 
to  be  exactly  two  inches  long,  without  the  necessity  of  their 
being  actually  measured,  is  as  follows  :  f 

An  eight-inch  triangle  (Fig.  27),  was  so  constructed  that  its 
center  was  definitely  located  by  making  it  of  parallel  pieces  of 
steel,  J  inch  thick  and  If  inch  wide,  accurately  scraped  and  fitted 
together.  Within  this  triangle,  its  inner  sides  tangent  to  the 
circumference,  was  fitted  a  cylindrical  plug  or  center.  This  plug 
having  been  turned  upon  a  true  mandrel,  the  condition  of  the  hole 
passing  through  it  exactly  in  the  center,  naturally  took  care  of  itself. 
A  second  cylindrical  plug,  hardened  and  ground,  was  next  fitted 
to  the  center  plug.  This  hardened  cylinder  was  ground  to  size 
exactly  equal  to  the  diameter  of  the  largest  circle  which  can  be  in- 
scribed in  an  equilateral  triangle,  the  sides  of  which  are  two  inches. 
Its  diameter  is,  therefore,  f  -/3,  or  1.1547  inches. 

*  See  page  97,  ante. 

t  See  aleo  page  161  for  further  description  of  the  construction  of  this  master  triangle. 


145 

By  securely  holding  a  triangular  piece  of  hardened  steel  ^  in. 
thick  (Fig.  18),  upon  the  stud  passing  through  the  center  plug, 
and  having  its  faces  or  sides  reversed  in  position  as  regards  the 
sides  of  the  large  triangle,  the  sides  are  each  ground  parallel 
to  the  opposite  sides  of  the  master  triangle,  and  also  ground  until 
a  sharp-edged  corrected  square,  held  against  the  side  of  the  large 
triangle,  determines  the  tangency  of  the  sides  to  the  inscribed 
circle  1.1517  inches  in  diameter. 


FIG.  18. 

As  the  large  triangle  is  carefully  tested  for  equality  of  angles,., 
this  inscribed  circle  furnishes  the  remaining  data  for  producing., 
a  triangular  model  whose  sides  are  known  to  be  each  two  inches- 
long,  without  the  necessity  of  their  being  actually  measured. 
In  fact  it  would  be  impossible  to  measure  them  in  any  other- 
known  way  within  the  limit  which  this  method  makes  entirely 
practicable,  and  which  at  the  same  time  "  fortifies  "  each  step  in* 
the  process,  by  employing  fundamental  principles,  and  keeping, 
the  limit  of  error  within  what  is  claimed,  which  is  TO^O  °f  an' 
inch.  Imagine  any  one  measuring  the  sides  of  such  a  two-inch 
triangle  by  actual  contact  with  the  almost  infinitely  sharp  edges^ 
where  the  sides  must,  theoretically,  meet ;  I  venture  to  say  no- 
two  readings  would  agree,  and  it  is  certainly  safe  to  assume  that 
each  succeeding  measurement  would  become  less  and  less,  as 
these  fine  edges  were  destroyed  by  this  unavoidable  contact. 

In  the  method  described,  using  the  inscribed  circle,  it  is  not 
necessary  to  have  any  edge  whatever,  as  we  may  feel  certain  that 
the  length  of  the  sides  would  be  two  inches  if  prolonged  to  meet, 
each  other.  For  the  purpose  intended,  it  does  not  matter  if  these 
edges  are  blunt  or  even  more  or  less  trun.cat.ed,  as  it  is  the  position,. 
10 


146 

and  not  the  actual  length  of  the  sides,  which  it  is  necessary  to 
establish. 

In  order  to  have  the  flat  of  the  thread  correct  for  such  a  pitch, 
in  this  case  taking  two  inches  as  a  base  from  which  to  start,  the 
flat  of  which  would  be  one-quarter  of  an  inch  or  one-eighth  of 
two  inches,  the  method  adopted  is  as  follows :  The  altitude  of 
the  frustum  of  this  triangle  was  obtained  after  having  removed 
the  smaller  triangle  at  the  top,  the  sides  of  which  are  one-quarter 
of  an  inch,  by  subtracting  the  altitude  of  this  small  triangle 
from  the  total  altitude  of  the  equi-angular  two-inch  model,  which 
gave  the  distance  from  the  base  to  the  top  of  this  truncated 
triangle.  By  having  this  measured  exactly,  the  top  and  bottom 
planes  being  parallel  to  each  other,  this  distance  came  naturally, 
and  evidently  must  be  one-quarter  of  an  inch  without  the  neces- 
sity of  its  being  measured.  The  actual  measurement  of  this 
quarter-inch  flat  would  evidently  be  very  difficult,  because  we 
are  dealing  with  the  edges  formed  by  obtuse  angles,  and  the 
accuracy  obtainable  would  certainly  not  be  within  the  limit 


FIG.  19. 

which  is  required.  After  this  triangle  was  established,  a  microm- 
eter was  made,  which  we  have  before  us  (Fig.  19),  in  which  the 
model  two-inch  triangle  is  used  to  determine  the  extreme  limit 
through  which  the  micrometer  jaw  shall  move ;  establishing  a 
"  zero,"  if  it  may  be  so  called,  for  a  starting  point,  the  jaw  of  the 
•caliper  moving  towards  the  smallest  possible  flat  that  might  be 
measured,  or  that  would  be  required  for  the  finest  pitches.  This 
;inicrometer  is,  as  its  name  implies,  a  divided  circle  and  a  screw, 
.measuring  very  small  advances  of  the  jaw.  In  order  to  verify 


147 

these  subdivisions,  lines  were  ruled  by  Professor  Rogers,  four 
hundred  to  the  inch,  with  a  diamond,  upon  the  polished,  hard- 
ened surface  of  the  center  of  the  bar. 

There  being  250  divisions  graduated  upon  the  index  circle, 
and  the  pitch  of  the  screw  being  ?V  of  an  inch,  each  division 
represents  Tff!oir  of  an  inch. 

Each  of  the  lines  ruled  400  to  the  inch  upon  the  sliding  bar 
serves  to  check  or  correct  the  readings  of  every  25th  division  of 
the  graduated  circle,  and  thus  to  provide  corrections  for  possible 
errors  in  the  screw. 

By  the  use  of  this  micrometer  one  can  accurately  measure  the 
flats  of  the  tools  which  are  used  to  cut  the  United  States  Standard 
or  Franklin  Institute  thread  of  any  number  of  threads  per  inch. 

In  order  to  show  the  adaptation  of  this  form  of  thread  to 
interchangeable  work,  and  also  to  demonstrate  its  extreme  sim- 
plicity as  a  basis  for  an  interchangeable  system  of  screw  thread 
gauges,  we  have  (Fig.  20)  a  drawing  showing  how,  should  this 
thread  be  even  larger  in  diameter  on  the  outside,  but  with  the 
diameter  correct  in  the  angle  of  the  thread,  the  variation  of  this 
outside  diameter  from  that  of  a  standard  cylindrical  size  has  no 
effect  upon  the  fit  of  the  nut  which  may  be  screwed  upon  the 
standard  or  upon  a  bolt  representing  this  standard  size.  The 
only  difference  which  we  would  notice  is  that  the  top  of  the 
thread  would  'be  narrower,  and  consequently  the  top  would  be 
higher,  in  the  space  cut  away  by  the  tap.  Plence,  taps  that  are 


FIG.  20. 

made  for  tapping  nuts  with  the  United  States  Standard  thread, 
if  made  exactly  right  in  the  angle  of  the  thread,  that  is,  having 
the  angle  sixty  degrees,  and  the  diameter  measured  in  this  angle 
of  the  thread,  correct,  the  outside  diameter  has  no  effect,  within 


148 

certain  limits,  to  change  its  size,  merely  cutting  away  within  the 
nut  more  metal  outside  of  the  limit  of  one-eighth  the  pitch.  In 
the  case  of  the  bolt  which  fits  this  nut,  the  outside  diameter 
should  be  kept  standard,  the  space  between  the  bottom  of  the 
thread  of  the  nut  and  the  top  of  the  thread  of  the  bolt  allowing 
particles  of  dirt  to  lodge,  without  affecting  the  fit  of  the  screw. 
This  condition  is  often  applied  in  the  manufacture  of  taps,  and  has 
been  found  to  lengthen  the  life  of  the  tap  in  a  very  marked  degree. 

In  the  case  of  one  company  I  have  in  mind,  and  who  make 
small  bolts  and  nuts,  the  taps  they  use  being  about  three-six- 
teenths of  an  inch  in  diameter,  they  were  formerly  satisfied  to 
have  a  tap  cut  fifteen  or  sixteen  thousand  nuts  before  perceptible 
wear  occurred,  they  have  found  that  in  having  them  made  under 
the  conditions  just  mentioned,  instead  of  stopping  at  sixteen 
thousand,  they  now  cut  a  hundred  and  twenty  thousand  without 
practical  variation  in  the  size  of  the  nut  as  compared  with  the 
standard  gauge. 

As  an  instance  of  the  "  eternal  fitness  of  things,"  allow  me  to 
quote  from  Mr.  Forney's  Report*  at  the  convention  of  Master 
Car-Builders,  held  in  this  city  (Philadelphia),  in  June,  1882: 

"  It  is  worthy  of  note  that  a  remedy  for  the  evil  complained  of 
by  master  car-builders,  that  nuts  made  by  some  firms,  or  at  some 
shops,  would  not  screw  on  bolts  made  at  others,  at  first  baffled 
the  ability  of  the  most  prominent  manufacturers  of  tools  in  the 
country,  and  to  provide  an  adequate  remedy  it  was  necessary  to 
secure  the  assistance  of  the  highest  scientific  ability  in  the  coun- 
try, which  was  supplied  through  the  co-operation  of  the  Professor 
of  Astronomy  of  the  oldest  and  most  noted  institution  of  learning 
in  the  land. 

"  The  man  of  science  turned  his  attention  from  the  planets, 
and  the  measurement  of  distances  counted  by  millions  of  miles, 
to  listen  to  the  imprecation,  perhaps,  of  the  humble  car- repairer, 
lying  on  his  back,  and  swearing  because  a  f-inch  nut — 'a  leetle 
small' — will  not  screw  on  a  bolt  a  '  trifle  large.'" 

In  the  system  so  wonderfully  developed  by  Sir  Joseph  Whit- 

*  Report  of  the  Committee  of  the  Master  Car-Builders'  Association,  appointed  "to  investigate 
and  report  on  the  present  construction  of  screws  and  nuts  used  in  cars ;  and  the  amount  of 
accuracy  that  is  desirable  to  secure,  and  the  best  means  of  maintaining  it,  in  the  standard 
adopted  by  the  Association,  in  Richmond,  Va.,  June  15,  1871,"  etc. 

Submitted  at  the  annual  Convention,  in  June,  1882. 

(For  complete  Report,  reprinted,  see  page  59,  ante.) 


149 

worth  for  the  manufacture  of  machinery  by  the  use  of  inter- 
changeable gauges,  he  obtained  the  subdivision  of  the  yard  by 
making  three  foot  pieces  as  nearly  alike  as  was  possible,  and 
working  these  foot  pieces  down  until  each  was  equal  to  the 
others,  and  placing  them  end  to  end  in  his  millionth  measuring 
machine ;  the  total  length  of  the  three  foot  pieces  was  then  com- 
pared with  a  standard  end  measure  yard.  These  three  foot 
pieces  were  ground  until  they  were  exactly  equal  to  each  other, 
and  the  three  added  together  equal  to  the  standard  yard.  The 
subdivision  of  the  foot  into  inch  pieces  was  made  in  the  same  way. 

This  method  required  the  exercise  of  extreme  care,  and  also 
the  expenditure  of  an  enormous  amount  of  time,  while  in  the 
system  which  has  been  adopted  by  The  Pratt  &  Whitney  Com- 
pany, the  sizes  are  not  constructed  in  this  way,  but  ruled  lines, 
which  represent  the  subdivision  of  the  British  yard,  are  first 
investigated,  their  accuracy  determined,  and  corrections,  if  neces- 
sary, applied,  before  a  single  gauge  or  any  end-measure  is  made. 
This  method  of  investigation  you  will  remember  was  partially 
described  in  our  previous  lecture. 

One  can  readily  understand  what  an  unsatisfactory  task  it 
would  be  to  attempt  to  subdivide  a  yard,  or  even  a  foot,  into  end- 
measure  pieces  varying  by  sixteenths  of  an  inch,  say  from  a 
quarter  of  an  inch  to  four  inches,  sixty-one  in  all,  each  of  which 
to  fulfill  the  condition  of  being  exactly  an  aliquot  part  of  the 
standard  yard,  which  they  each  should  represent.  We  can  imag- 
ine the  difficulties  to  be  overcome  by  any  one  attempting  this 
work  by  the  subdivision  of  a  standard  foot,  using  the  method 
adopted  by  Whitworth  as  early  as  1834.  Without  having  a  line 
measure  to  which  to  refer,  this  standard  foot  —  providing  it  was 
standard  at  the  start  —  would  necessarily  be  duplicated  and  this 
copy  subdivided  into  two  parts,  each  representing  six  inches, 
equal  to  each  other  of  course,  and  together  equal  to  the  foot. 
Constant  reference  would  have  to  be  made  to  the  original 
standard  foot  piece,  which  would  obviously  result  in  more  or 
less  wear  of  the  end  surfaces.  Then  the  six  inches  would 
need  to  be  halved,  and  so  on  until  the  inch  was  obtained.  Then, 
in  order  to  prove  that  the  inch  was  one-twelfth  of  the  foot, 
it  would  be  necessary  to  make  twelve  of  these  inches,  or  six 
inches  equal  to  the  six-inch  piece,  and  the  sum  of  all  to  be  equal 


150 

to  twelve  inches,  or  the  original  foot.  We  can  all  of  us  realize 
that  more  or  less  wear  has  resulted,  reducing  the  length  of  the 
standard  foot  in  the  course  of  this  constant  reference  to  it  as  the 
original  standard.  Providing,  even,  that  all  these  subdivisions 
were  carefully  made,  and  that  no  wear  perceptible  had  occurred 
to  the  original  standard,  we  are  still  not  below  an  inch. 

Subdivisions  into  quarters  and  sixteenths  would  still  further 
complicate  the  matter,  and  should  the  tentative  subdivision  be 
complete,  providing  the  operator's  patience  or  even  life  held  out, 
he  would  then  not  be  positive  that  he  had  even  the  inch  a  stand- 
ard, having  by  this  time  worn  appreciably  his  Original  standard 
foot  during  the  long  and  tedious  process  of  comparison  and  refer- 
ence necessary. 

Hence  a  definite  line-measure  is  really  the  only  reliable  means 
of  preserving  a  constant  and  standard  size,  and  it  is  this  princi- 
ple, which,  practically  carried  out,  has  been  the  means  of  produc- 
ing results  which  so  far  seem  to  fulfill  all  the  requirements  nec- 
essary for  an  accurate  system  of  interchangeable  gauges. 

In  order  to  help  out  the  matter,  in  the  method  of  subdivision 
by  trial,  recourse  must  be  had,  for  further  subdivision,  to  the  use 
of  a  screw  and  a  divided  micrometer  index  circle.  Just  here  we 
introduce  the  use  of  what  has  long  been  considered  one  of  the 
impossibilities  to  be  obtained  by  mechanical  skill  —  a  perfect 
screw.  It  was  upon  this  that  Whitworth  was  obliged  to  depend 
in  obtaining  his  subdivisions  by  sixteenths.  We  have  before  us 
upon  the  screen*  a  perspective  view  of  the  celebrated  Whitworth 
millionth  measuring  machine,  designed  and  used  by  Sir  Joseph 
Whitworth  to  measure  minute  differences  of  inch  standards. 
This  machine,  as  you  will  see,  combines  the  use  of  a  screw  for 
obtaining  slight  advances  of  the  measuring  faces  of  the  instru- 
ment, a  divided  micrometer  circle,  and  also  a  worm  wheel  to  still 
farther  magnify  slight  variations  of  position  of  the  measuring 
faces  of  this  carefully  constructed  micrometer. 

We  have  here  a  sectional  view  of  this  machine,  showing  the 
method  of  providing  against  back  lash  of  the  nut  and  screw, 
which  is  secured  by  a  double  nut,  as  shown  (Fig.  21)  in  the  repro- 
duction of  the  drawing  before  us.f  You  will  notice  that  the 

*  (Not  here  illustrated;  see  Fig.  21.) 

t  See  The  Whitworth  Measuring  Machine,  by  Goodeve  and  Shelley.    London,  1877. 


151 

machine  is  very  massive,'  and  the  accuracy  with  which  it  was 
constructed  is  designed  to  indicate  with  extreme  delicacy  differ- 
ences between  any  two  standard  inch  pieces,  so  called.  Between 


FIG.  21. 

the  end  or  face  of  the  rectangular  bar  which  advances  by  means 
of  the  screw  and  nut,  and  the  standard  end-measure  piece,  is  a 
small  polished  piece  of  steel,  having  parallel  faces,  called  a  "  feel- 
ing piece."  The  difference  in  length  of  two  end-measure  stand- 
ards is  detected  by  the  variation  in  the  reading  of  the  divided 
wheel,  and  the  uniformity  of  contact  is  indicated  by  means  of 
this  feeling  piece. 

The  tightness  of  an  end-measure  inch  which  is  only  one  mil- 
lionth of  an  inch  longer  than  one  to  which  the  machine  had  pre- 
viously been  adjusted,  will,  it  is  claimed,  prevent  this  feeling 
piece  from  dropping  when  placed  between  the  caliper  jaw  and 
the  standard. 

In  order  to  make  gauges  for  shop  use,  and  to  make  them  ot 
such  a  shape  as  to  be  practicable  and  not  readily  worn  through 
constant  reference,  Whitworth  proposed  a  form  of  cylindrical 
gauges  represented  by  plugs  and  rings.  These  standard  plugs 
he  measures  in  his  machine,  duplicating  his  end-measure  sizes  in 
this  more  serviceable  form. 

In  using  his  measuring  machine,  he  has  not  claimed  it  to  be  an 
instrument  for  originating  sizes,  but  merely  for  comparison  of 
minute  differences.  Hence,  in  order  to  maintain  a  constant  stand- 
ard, reference  must  be  had  to  end-measures  which  are  certainly 
liable  to  sustain  some  slight  change  from  wear  or  oxidation. 


152 

As  already  stated,  the  method  adopted  by  The  Pratt  &  Whit- 
ney Company,  and  which  was  proposed  originally  by  Professor 
Rogers,  is  that  of  making  gauges  to  correspond  to  line-measures 
which  are  accurate  subdivisions  of  the  imperial  yard,  thus  obvi- 
ating this  liability  to  wear. 

The  gauges  are  made  by  referring  each  separate  standard  to  a 
line-measure  ruled  upon  hardened  steel  which  has  a  rate  of 
expansion,  due  to  variations  of  temperature,  the  same  as  that  of 
the  hardened  steel  gauges  with  which  it  is  compared.  In  mak- 
ing any  number  of  gauges  of  the  same  size,  this  method  will 
ensure  the  last  gauge  being  exactly  the  same  as  the  first,  without 
reference  to  each  other  or  to  any  other  perishable  standard.  This 
has  actually  been  done  in  the  work  so  carefully  gone  through  by 
the  company,  and  it  is  possible  and  entirely  practicable  to  pro- 
duce gauges  so  nearly  alike,  by  this  means,  that  a  variation 
between  any  two  of  even  one  forty  or  one  fifty-thousandth  of  an 
inch  is  eliminated.  We  have  found  from  our  own  experience 
that  tool-makers  are  very  critical.  They  wrork  closer  than  they 
themselves  imagine,  and  in  duplicating  parts  of  any  machine  or 


FIG.  22. 

any  work  requiring  this  exactness,  they  work  often  wTithin  a 
limit  of  a  fifty-thousandth  of  an  inch  without  being  aware  of  the 
fact ;  so  that,  in  making  a  number  of  gauges  of  the  same  size,  it  is 
certainly  necessary  that  they  should  be  made  within  this  limit. 
Nothing  could  throw  more  gloom  over  the  spirits  of  a  manufac- 
turer of  gauges  than  the  discovery  that  a  tool-maker  is  able  to 
prove  conclusively  that  two  of  his  gauges,  when  new,  and  both 
marked  alike,  are  unlike  in  size. 

In  the  illustration  before  us  (Fig.  22),  we  have  a  form  of  a 


153 

simple  bench  micrometer  or  measuring  machine,  in  which  the 
screw  and  subdivided  index  circle  form  the  main  features.* 

In  order  to  obtain  practically  the  same  result,  in  duplicating 
sizes  from  a  standard  for  ordinary  gauge  work,  auxiliary  faces 
or  caliper  jaws  are  used,  and  are  shown  at  the  left  of  the 
measuring  faces.  These  auxiliary  jaws  serve  to  hold  a  small 
cylindrical  plug,  so  that  in  adjusting  the  machine  or  caliper  to 
any  given  size,  the  pressure  between  the  caliper  jaws  in  which 
this  standard  is  placed  can  be  determined  by  the  tightness  or 
position  of  this  small  cylindrical  plug.  By  taking  the  reading  on 
the  micrometer  and  bringing  a  second  gauge  in  contact  in  place 
of  the  original,  the  same  conditions  of  pressure  upon  this  second 
gauge  may  be  readily  determined,  by  noting  the  behavior  of  this 
little  "  feeling  piece,"  as  Whitworth  might  call  it.  The  varia- 
tion may  then  be  read  in  the  ordinary  way  by  the  subdivisions 
upon  the  divided  index  circle.  As  an  instrument  for  originating 
a  size,  even  with  a  screw  of  the  utmost  precision,  it  could  not 
be  expected  to  be  infallible,  the  limit  of  error  being  about  -s^irs 
of  an  inch  ordinarily  ;  but  to  copy  or  duplicate  sizes  it  has  been 
found  to  be  very  serviceable.  A  variation  as  minute  as  one 
hundred-thousandth  of  an  inch  has  been  shown  to  be  appreciable 
in  cases  which  have  come  under  my  own  observation. 

In  order  to  make  standard  gauges  within  the  limit  of  accuracy 
necessary  for  interchangeability,  and  to  fulfill  the  requirements 
of  modern  work-shop  practice,  it  may  be  unqualifiedly  stated  that 
line  measure,  adapted  for  use  as  an  ultimate  practical  reference 
standard,  is  the  best  for  this  purpose.  The  strong  reason  for  this 
statement  is  that  the  ever  present  element  of  wear  from  constant 
use  is  entirely  eliminated. 

The  standard  line-measure  bar  we  now  have  before  us  (Fig.  23), 
is  one  which  has  certainly  shown  this  to  be  not  only  a  strong 
reason,  but  a  valid  one.  The  lines,  which  represent  aliquot  sub- 
divisions of  the  Imperial  yard,  were  ruled  upon  a  dividing  engine 
constructed  by  Professor  Rogers,  the  work  being  done  at  the 
factory  of  the  American  Watch  Company,  at  Waltham,  Mass. 

The  total  length,  represented  by  the  defining  lines,  is  exactly 
one-ninth  of  the  length  of  the  Imperial  Yard,  or  four  inches,  hav- 
ing no  correction  at  62°  F.  In  other  words,  it  is  within  a  limit 

*See  also,  page  205,  Illustrated  Catalogue,  January  1886,  The  Pratt  &  Whitney  Company. 


154 

of  ToAiro  °f  an  inch.*  "The  subdivisions  are  inches,  half  inches, 
quarters,  eighths,  and  sixteenths  along  one  edge,  and  a  band  of 
lines,  2,500  per  inch,  extending  two  inches  from  one  end.  Next 
is  ruled  a  series  of  lines  representing  the  exact  bottom  diameters 
or  "  tap  sizes  "  of  all  United  States  standard  thread  gauges  from 
i  in.  to  4  inches  inclusive. 


51    I 


1 1 1  I  II 


FIG.  23. 

Along  the  edge  opposite  the  series  of  sixteenths,  are  traced 
lines  representing  tenths  and  twentieths  of  an  inch,  also  covering 
a  space  of  two  inches.  This  bar  is  made  of  steel,  hardened  and 
ground  perfectly  plane  on  its  upper  surface  and  highly  polished. 
The  graduated  lines  were  transferred  to  this  surface  using  a  metric 
screw,  the  pitch  of  this  screw  being  one-half  a  millimeter.  The 
ruling  was  done  with  a  diamond.  So  carefully  was  the  relation  be- 
tween the  value  of  the  pitch  of  this  metric  screw  and  the  length  of 
the  yard  determined  by  Professor  Rogers,  that  upon  investigation, 
using  the  method  of  the  "  stops,"  mentioned  in  our  previous  lec- 
ture (page  137),  the  greatest  error  in  any  ruled  subdivision  was 
found  to  be  within  a  limit  of  ^oifo ¥  of  an  inch  for  the  particular 
subdivision  of  the  Imperial  yard  which  each  should  represent. 

When  we  realize  that  the  transfer  of  each  separate  line,  except 
the  band  of  2,500  per  inch  (this  band  being  carefully  checked 
during  the  operation  of  ruling),  was  an  actual  computed  setting 
of  the  diamond  before  the  line  was  traced,  some  idea  may  be 
obtained  of  the  wonderful  precision  of  the  mechanism  of  the 
dividing  engine,  as  well  as  the  correctness,  and  pains  taken,  in 
the  mathematical  calculations  involved. 

Being  hardened  steel,  the  measurement  of  hardened  steel 
gauges,  by  being  referred  to  it,  becomes  entirely  practicable  at 
any  convenient  temperature,  providing,  of  course,  that  an  equal 
temperature  for  both  standard  bar  and  gauge  is  maintained.  As 
the  lines  are  less  than  -^-s^w  of  an  inch  in  width,  all  comparisons 
must  be  made  using  a  microscope  of  a  ordinarily  high  power. 

The  practicability  of  "  calipering  "  under  a  microscope  has  long 
been  urged  by  Professor  Rogers  as  being  the  only  exact  method 

*See  Prof.  Rogers1  Report,  page  46,  ante. 


155 

of  inspecting  standard  gauges.  The  results  obtained  by  the  use  of 
this  method,  combining,  as  it  does,  science  and  practice,  have 
demonstrated  beyond  any  question,  the  simplicity,  as  well  as  the 
accuracy  of  the  method.  To  give  some  idea  of  its  value  for  the 
purposes  of  originating  standard  sizes,  an  instance  in  mind  may 
be  stated. 

A  number  of  cylindrical  size  gauges,  external  and  internal, 
commonly  called  plugs  and  rings,  a  representation  of  which  is 


FIG.  24. 

shown  in  Fig.  24,  were  made.  They  wrere  finished  to  agree  with 
the  subdivisions  upon  this  little  hardened  steel  line-measure 
standard.  Nearly  eighteen  months  afterward,  a  new  lot  of  the 
same  sizes  were  made,  and  upon  trial  it  was  shown  that  any  ring 
of  the  first  lot  fitted  perfectly  any  plug  of  the  second.  Both  lots 
had  been  made  without  reference  to  any  intermediate  standard 
set  of  plugs,  except  to  "  rough  them  out,"  as  it  is  called,  within 
about  T  oto~o  °f  an  inch,  all  finishing  after  this  having  been  done 
from  data  determined  by  calipering  under  the  microscope.  * 

A  good  gauge  fit  is  not  that  the  ring  shall  slide  freely  over  the 
plug  without  perceptible  "  shake,"  but  one  such  that  the  ring, 
when  well  lubricated  with  sperm  or  other  good  oil,  shall  move 
easily  after  having  it  fairly  on  the  plug,  showing  no  tendency  to 
"  grip  "  the  plug  while  the  ring  is  kept  in  motion.  Let  the  ring, 
however,  stop  moving  even  for  a  few  seconds,  and  this  condition 
of  an  apparently  easy  fit  is  suddenly  changed  to  &  driving  fit,  often 
causing  serious  damage  to  the  plug  or  ring  in  separating  them. 
In  order  to  show  this  condition  of  perfect  fit  to  best  advantage, 
the  temperature,  of  course,  must  be  the  same  for  both.  The 
surfaces  of  the  plug  and  ring  must  be  as  hard  as  steel  can  be 
made,  and  polished  as  carefully  as  the  state  of  the  art  will  admit. 
A  good  way  of  testing  the*  accuracy  of  any  set  or  pair  of  cylin- 
drical gauges  in  reference  to  their  being  aliquot  parts  of  any 
adopted  standard,  is  to  place  within  a  ring  which  fits  a  standard 
plug,  two  smaller  size-gauges  tangent  to  each  other,  and  if  their 

*  See  Fig.  15,  page  133. 


156 

sum  is  equal  to  the  diameter  of  the  larger  single  gauge  they  will 
be  tangent  to  the  ring  also.  If  exactly  right,  they  will  be  found 
to  hold  together  tightly,  as  the  elements  of  the  cylinders  which  are 
in  contact  must  either  occupy  the  same  space  or  be  compressed 
enough  to  allow  this  practical  tangency  to  be  made.  Care  must 
be  taken  not  to  force  the  second  gauge  in  too  far,  as  this  would 
evidently  tend  to  injure  them. 

In  the  gauges  before  us,  which  are  2i,  li,  and  1  inch,  we  may 
see  how  nicely  this  test  is  met.  If  we  now  use  a  gauge  which 
is  J^VTJ-  of  an  inch  smaller  than  one  inch  in  diameter,  in  the  addi- 
tion to  2J  inches,  the  tangency  is  incomplete,  for  this  gauge  drops 
through,  hardly  touching. 

A  thousandth  of  an  inch,  you  may  say,  is  almost  not  worth 
considering,  but  here  we  have  a  standard  plug  and  ring,  the  ring 
fitting  perfectly,  as  you  see.  We  now  insert  the  plug  which  is 


FIG.  25. 

of  an  inch  too  small ;  it  can  be  literally  thrown  on  or 
off,  one  might  even  say  that  it  "  fairly  rattles,"  the  difference 
seems  so  great  as  compared  with  the  fit  of  the  standard. 

We  have  here  a  f -inch  plug  which  is  only  I^-^-Q  of  an  inch  smal- 
ler than  standard,  the  plug  and  ring  representing  which  we  also 
have.  You  will  notice  it  is  not  so  loose  as  was  the  inch  plug 
which  is  roVo-  of  an  inch  small,  but  still  less  than  one-third  of  this 


157 

minute  difference  is  perceptible,  and  shows  plainly  that  it  does 
not  perfectly  fit  the  ring. 

In  our  experience  in  the  manufacture  of  standard  gauges,  even 
this  test  is  not  a  delicate  nor  an  entirely  satisfactory  one.  It  is 
not  equal  to  that  obtained  by  the  use  of  a  fixed  caliper  gauge  of 
drop  forged  steel,  having  polished  parallel  jaws,  a  specimen  gauge 
of  this  form  being  represented  in  Fig.  25. 

For  the  purpose  of  testing  the  larger  sizes,  this  latter  form  of 
gauge  is  the  best,  as  the  friction  between  the  two  surfaces  of  cyl- 
indrical gauges  is  decidedly  a  variable  quantity,  depending  upon 
the  degree  of  hardness  and  polish  of  the  fitting  surfaces  of  plug 
and  ring.  It  is  also  possible  that  the  cohesive  force  which  we  have 
already  mentioned  may  act  in  this  close-fitting  relation,  explain- 
ing why  the  ring  should  suddenly  be  so  tightly  "  gripped,"  when 
allowed  to  remain  together. 

With  a  two-inch  gauge,  a  variation  of  -g^fa-is  of  an  inch  is  im- 
perceptible when  a  ring  is  used  to  determine  this  small  differ- 
ence, while  with  a  caliper  gauge  made  as  just  described,  having 
polished  parallel  jaws,  this  minute  difference  may  be  readily 
detected,  if  the  caliper  be  first  carefully  adjusted  to  a  standard 
two-inch  cylindrical  gauge. 

To  convey  some  idea  of  the  minute  variation  which  may  thus 
be  detected,  I  may  state  that  a  fragment  of  gold  leaf,  so  thin  that 
a  mere  touch  of  the  fingers  caused  its  total  disappearance,  on 
being  carefully  measured  under  the  microscope,  showed  that  its 
average  thickness  was  7Trj ririr  of  an  inch. 

This  same  gold  leaf  would  actually  float  in  the  air  like  a  spider's 
web,  and  yet  this  extreme  "  thinness,"  if  it  may  be  so  termed,  is 
actually  twice  the  amount  of  the  limit  of  error  within  which  it  is 
possible  to  duplicate  hardened  standard  plug  gauges,  by  "  lapping," 
or  grinding,  referring  them  to  a  line-measure  under  the  microscope. 

To  convey  some  idea  of  the  minuteness  of  the  lines  and  the 
spaces  between  them,  of  the  lines  ruled  upon  this  standard  line- 
measure  bar  in  the  space  covered  by  the  first  two  inches,  2,500 
per  inch,  they  would,  if  placed  one  inch  apart,  the  lines  being 
magnified  in  proportion,  be  represented  by  furrows  or  marks  one- 
tenth  of  an  inch  wide,  and  would  extend  over  a  length  of  416 
feet  8  inches,  or  nearly  one-twelfth  of  a  mile. 

Before  concluding,  it  might  be  well  to  refer  to  work  requiring 
only  an  ordinary  degree  of  accuracy,  though  none  the  less  impor- 


158 


tant  in  its  way.  The  measurement  of  the  diameter  of  drawn 
wire  has  long  been  a  matter  of  confusion,  owing  to  the  use  of 
numbers  to  designate  arbitrary  sizes,  which  in  many  cases  do  not 
correspond  with  each  other  for  the  same  numbers  used  in  differ- 
ent standards  or  styles  of  fixed  wire  gauges.  Even  wire  gauges 
of  the  same  standard  do  not  agree  with  each  other,  due  perhaps 
to  wear,  if  not  from  actual  variation  of  the  gauges  when  new. 
To  overcome  this  serious  difficulty,  the  use  of  the  micrometer, 
indicating  thousandths  of  an  inch  for  wire  and  sheet  metal 
measurement,  was  adopted  by  the  Association  of  Master-Mechan- 
ics, in  Convention  at  Niagara  Falls,  June,  1882. 

Since  this  date,  in  England,  the  Standards  Department,  Board 
of  Trade,  has  issued  a  table  of  wire  gauge  sizes  to  be  the  legal 
standard  on  and  after  March  1st,  1884.  In  the  table  just  men- 
tioned, and  herex  given,  the  numbers  are  retained,  but  each  num- 
ber must  represent  exactly  a  certain  diameter  in  thousandths  of 
an  inch.  The  table  is  also  extended  to  include  the  metric  system 
by  placing  opposite  each  size,  in  thousandths  of  an  inch,  its  value 
in  millimeters,  carried  out  decimally  to  tenths  of  a  millimeter. 

IMPERIAL   STANDARD   WIRE  GAUGE. 
[In  effect,  March  1,  1884.] 

BIRMINGHAM 


BIRMINGHAM 

DI 

WIRE  GAUGE  NO. 

IN. 

7/0 

0.500 

6/0 

.464 

5/0 

.432 

4/0 

.400 

3/0 

.372 

2/0 

.348 

0 

.324 

1 

.300 

2 

.276 

3 

.252 

4 

.232 

5 

.212 

6 

.192 

7 

.176 

8 

.160 

9 

.144 

10 

.128 

11 

.116 

12 

.104 

13 

.092 

14 

.080 

15 

.072 

16 

.064 

17 

.056 

18 

.048 

19 

OA 

.040 

flQA 

£() 

21 

.Oo6 
.032 

22 

.028 

DIAMETER. 


MM.       WIRE  G> 

12.70 

23 

11.78 

24 

10.97 

25 

10.16 

26 

9.45 

27 

8.84 

28 

8.23 

29 

7.62 

30 

7.01 

31 

6.40 

32 

5.89 

33 

5.38 

34 

4.88 

35 

4.47 

36 

4.06 

37 

3.66 

38 

3.26 

39 

2.95 

40 

2.64 

41 

2.34 

42 

2.03 

43 

1.83 

44 

1.63 

45 

1.42 

46 

1.22 

47 

1.01 

48 

0.91 

49 

0.81 

50 

0.71 

DIAMETER. 

IN. 

MM. 

0.024 

0.61 

.022 

0.56 

.020 

0.51 

.018 

0.45 

.0164 

0.42 

.0148 

0.38 

.0136 

0.35 

.0124 

0.31 

.0116 

0.29 

.0108 

0.27 

.0100 

0.25 

.0092 

0.23 

.0084 

0.21 

.0076 

0.19 

.0068 

0.17 

.0060 

0.15 

.0052 

0.13 

.0048 

0.12 

.0044 

0.11 

.0040 

0.10 

.0036 

0.09 

.0032 

0.08 

.0028 

0.07 

.0024 

0.06 

.0020 

0.05 

.0016 

0.04 

.0012 

0.03 

.0010 

0.025 

159 

Tins  table,  for  instance,  begins  with  No.  7/0,  which  is  .500  of 
an  inch  in  diameter,  or  12.7  millimeters.  No.  1  is  .300  of  an  inch, 
and  No.  50,  the  smallest  in  the  list  of  sizes,  is  .001  of  an  inch. 
The  range,  therefore,  is  from  one-thousandth  of  an  inch  to  one- 
half  of  an  inch.  The  variations  are  irregular,  not  advancing  by 
equal  amounts  for  each  succeeding  larger  size.  This  is  no  doubt 
due  to  the  effort  to  retain,  as  nearly  as  possible,  a  general  average 
of  the  old  wire-gauge  sizes.  In  every  case,  however,  the  exact 
size  is  stated  in  thousandths  of  an  inch,  or  the  decimal  parts  of 
the  meter. 

The  feeling  in  regard  to  the  great  lack  of  a  uniformity  in  wire- 
gauge  sizes,  under  the  old  notched  gauge  system,  may  be  best 
expressed  by  a  remark  recently  made  by  the  master  mechanic  of 
one  of  our  best  Eastern  railroads.  He  said  that  any  one  would 
be  as  likely  to  go  to  a  lumber-yard  and  order  a  plank  ten  feet 
long,  twelve  inches  wide,  and  as  "  thick  as  a  notch  cut  in  a  fence 
post  made  by  Tom  Jones,"  as  to  think  of  ordering  sheet  metal, 
specifying  that  it  should  be  simply  "  No.  13  wire  gauge,"  as 
has  often  been  done,  not  even  stating  what  particular  u  standard  " 
gauge  it  is  so  called. 

The  application  of  Standards  of  Length  to  ordinary  workshop 
practice  has  so  wide  a  range  that  it  would  be  impossible,  in  the 
time  at  our  disposal  this  evening,  to  attempt  an  enumeration  of 
the  many  forms  of  gauges  and  templates  necessary  to  secure  the 
three  important  elements  we  have  already  mentioned,  —  "cheap- 
ness, serviceableness,  and  quantitative  accuracy," —  even  in  a  sin- 
gle department  of  work  requiring  interchangeability  of  parts, 
as,  for  instance,  the  manufacture  of  sewing-machines,  or  the 
results  obtained  by  the  use  of  standard  gauges  in  the  manufac- 
ture of  firearms. 

It  must  not,  however,  be  understood  that  all  work  produced 
by  the  use  of  a  system  of  standard  interchangeability  is  as 
perfectly  in  duplicate  as  are  the  gauges  to  which  they  are  referred. 
The  gauges  are  the  means  provided  for  keeping  within  certain 
definite  bounds  in  the  production  of  thousands  of  pieces  of  the 
same  size  or  shape,  in  which  oftentimes  a  certain  amount  of  vari- 
ation is  allowed,  both  plus  and  minus. 

Standard  gauges  prevent  the  gradual  slipping  away  from  the 
original  size  and  serve  to  bring  back  within  the  necessary  limit, 


160 

variations  of  size  which  would  cause  endless  trouble,  and  no 
small  loss  in  the  final  assembling  of  these  intended  interchange- 
able parts. 

This  accurate  fitting  is  really  only  necessary  in  gauge  work, 
for  if  bearings  or  other  parts  of  machinery  were  as  closely  made, 
they  would  not  move,  or  if  bjr  applying  power  enough  they 
should  be  started,  the  absence  of  oil  and  the  effect  of  the  cohe- 
sion, if  we  may  be  allowed  to  say  it,  would  quickly  ruin  the  sur- 
faces in  contact;  hence  a  certain  amount  of  freedom  must  be 
allowed.  By  making  the  journals  and  the  bearings  in  which 
they  are  to  run  to  certain  definite  sizes  for  each,  the  journal  as 
many  thousandths  or  ten-thousandths  of  an  inch  smaller,  as  the 
size  or  length  of  bearing  may  require,  referring  each  to  some  par- 
ticular gauge  as  a  standard,  no  fear  need  be  entertained  that 
other  than  a  satisfactory  fit  will  be  the  practicable  result. 

Before  concluding,  brief  mention  should  be  made  of  the  neces- 


FIG.  26. 

sity  of  definite  action  to  secure  uniformity  in  gauge  dimensions 
for  steam  and  gas  pipe  thread  and  fittings  ;  a  standard  for  which  is 
now  claiming  the  serious  attention  of  manufacturers  and  users  of 
pipe  and  pipe  fittings  in  this  country,  and  also  in  England.* 
Pipe  ^thread  dimensions,  when  permanently  established  in  the 
form  of  standard  gauges  (Fig.  26),  made  so  by  referring  them  to 
accurate  subdivisions  of  the  Imperial  yard,  though  seeming  to 

*Since  authoritatively  settled  by  the  legislation  of  the  Association  of  Wronght-Iron  Pipe 
Manufacturers,  October  27,  1886,  and  the  Manufacturers'  Association  of  Brass  and  Cast  Iron  Fit- 
tings, December  8,  1886,  in  adopting  the  Briggs  Standard. 

See  Report  of  Committee  on  Standard  Pipe  and  Pipe  Threads,  Am.  Soc.  Mech.  Engineer?, 
Vol.  VIII.  Transactions. 


161 

be  an  unnecessary  refinement  for  so  ordinary  a  class  of  work, 
really  furnishes  the  true  means  of  placing  upon  a  sound  basis, 
and  of  extending  the  already  well-developed  and  recognized  prin- 
ciple of  modern  manufactures,  which  is  "cheapness,  serviceable- 
ness,  and  quantitative  accuracy." 


The  following  is  a  description  of  the  method  employed  by  The 
Pratt  &  Whitney  Company  in  establishing  the  angle  and  width 
of  flat  of  the  top  and  bottom  of  the  thread  of  gauges  represent- 
ing the  United  States  Standard  system,  reprinted  in  extract,  with 
some  revision,  from  an  article  by  Mr.  J.  "W.  Heyer,  published  in 
Mechanics,  Jan.  13,  1883: 

The  correct  conditions  to  be  established  mechanically  were  —  first, 
the  angle,  which  is  60  degrees;  second,  the  width  of  the  flat  on  the  top 
and  bottom  of  the  thread,  which  is  one-eighth  of  the  pitch;  and  third, 
the  number  of  threads  per  inch,  which  is  determined  by  means  of  a 
formula,*  and  must  be,  in  a  correct  gauge,  as  nearly  a  perfect  screw  as 
can  be  obtained  by  machine  methods. 

A  method  of  obtaining  the  first  condition,  or  of  making  by 
machined  work  an  equilateral  triangle  closely  to  mathematical  lines,  was 
designed  by  the  writer,  and  was  used  also  for  the  purpose  of  estab- 
lishing a  "zero"  or  positive  starting  point  from  which  to  measure  the 
flats  on  the  tools  used  to  cut  the  various  United  States  Standard 
pitches,  so  that  if  a  gauge  is  made  having  the  correct  outside  diameter, 
the  thread  cut  to  the  proper  depth  and  the  correct  number  of  threads 
per  inch,  the  angle  of  the  thread  exactly  60  degrees,  and  the  lead  of 
the  screw  of  accurate  pitch,  a  tool  having  the  requisite  amount  of  flat 
on  the  point  will  leave  the  flat  on  the  top  of  the  thread  exactly  the 
same  width  as  that  of  the  flat  at  the  bottom  of  the  thread. 

Fig.  27  shows  two  views  of  an  equilateral  triangle  obtained  by 
machined  work,  and  which  was  originated  as  follows:  Three  bars  of 
steel,  each  8  inches  long,  were  made,  having  their  sides  parallel,  and 
equal  in  every  respect  to  each  other.  The  holes  in  the  ends-  of  the 
bars  were  placed  the  same  distance  apart  and  at  an  equal  distance  from 
either  edge  of  the  bars  by  means  of  templets  and  fixtures  shown  in 
Fig.  28,  in  which  S  represents  a  lathe  spindle,  and  c  a  lathe  center 
fitting  the  spindle,  the  center  being  turned  so  as  to  accurately  fit  a  bush, 
d,  made  of  steel.  A  rectangular  block,  e,  was  then  made,  having  a  slot 
fitting  the  bush,  d;  the  bars,  A,  A,  A,  also  accurately  fitted  this  slot. 

*  See  page  167,  (a). 
11 


162 

The  rectangular  block  was  then  firmly  fastened  to  the  face-plate  of  a 
lathe,  as  shown  in  the  figure,  and  a  hole  bored  in  it  exactly  the  same 


E 

I 

1 

1 

D 

i    i 

| 

1 

3 

yy 

, 

1          Mill 

1     IkJJ  ' 

|  1 

!;  ji 

^ 

r 
i 

i 

--,           v_^    ! 
1 
1                       i 

1  1 

0 

i 

1 

FIG.  27. 

size  as  that  in  the  bush,  thus  locating  the  hole  in  the  center  of  the  slot, 
and  at  right  angles  to  its  base.     This  rectangular  block  was  then  placed 


163 


on  the  lathe  center,  as  shown  in  Fig.  28,  and  each  bar  placed  in  this 
slot  and  firmly  bolted  to  the  face-plate  and  a  hole  then  bored  in  one 
end. 

A  parallel  piece,  /,  equal  in  thickness  to  the  base  of  the  block,  e,  was 
then  firmly  fastened  to  the  face-plate,  as  shown  in  the  cut.  This  piece 
was  used  to  bore  the  first  hole  in  the  bars  used  for  the  sides  of  this 
"master  triangle."  In  boring  the  second  hole  in  these  bars,  a  pin  was 
inserted  in  a  hole,  g,  in  the  parallel  piece,  /,  and  the  first  hole  in  each 
of  the  bars  fitted  this  pin. 

The  bars  A,  A,  A,  Fig.  27,  after  being  halved  at  the  ends  and  dow- 
eled together,  formed  an  equilateral  triangle,  mechanically  or  practi- 


FIG.  28. 

cally  perfect,  and  represented  a  triangle  machined  approximately  to 
mathematical  lines. 

In  Fig.  27,  B  is  a  bush  having  a  flange,  and  is  fitted  to  the  inside  of 
the  triangle,  being  screwed  and  doweled  to  the  bars,  A,  A,  A,  securing 
the  conditions  of  a  cylindrical  hole  accurately  located  in  the  center  of 
our  master  triangle.  The  bush,  B,  has  on  the  outside  of  the  flange  a. 
projection.  D,  a  hardened  steel  cylinder,  ground  to  the  diameter  of  an 
inscribed  circle  of  a  triangle  having  sides  of  two  inches,  this  diameter- 
being  1.1547  inches. 

A  small  triangular  piece  of  steel  having  a  hole  in  its  center,  of  the 
same  diameter  as  that  in  the  bush,  B,  which  fits  the  inner  sides  of  the 
large  triangle,  was  then  bolted  to  the  projecting  part  of  the  flange,  D, 


164 

•  as  shown  in  Fig.  27,  the  bolt  nicely  fitting  both  holes.  The  master 
triangle  was  then  placed  on  a  planer  and  strapped  to  a  right-angled 
"knee"  and  each  side  of  the  small  triangle  planed  to  the  dimensions 
represented  by  the  projecting  cylinder,  which,  as  stated,  is  1.1547 
inches  diameter. 

To  obtain  the  width  of  the  flat  at  the  top,  one-eighth  of  the  altitude 
of  the  small  triangle  was  planed  off  parallel  to  the  base,  leaving  a  flat 
which  is  exactly  one-quarter  of  an  inch  long.  (See  page  146.) 

The  flat  of  this  small  triangle  or  test  piece  thus  represents  the  width 
of  the  flat  of  the  thread  of  a  gauge  of  two  inches  pitch,  and  is  used 
in  a  micrometer  made  for  the  purpose  of  measuring  the  width  of  flat 
of  the  tools  used  to  cut  threads  of  any  number  per  inch,  from  the  small- 
est possible  to  make  up  to  the  largest  diameter  and  coarsest  pitch. 

Fig.  29  represents  this  micrometer,  which  has  a  screw  40  threads 
per  inch,  and  an  index  circle  divided  into  250  parts,  one  division 

TTT.Vinr  of  au  inch- 


FIG.  29. 

In  determining  the  "zero"  on  this  micrometer,  the  test-piece  trian- 
gle is  placed  between  the  jaws;  and  when  light  is  shut  out  from  the 
three  bearing  edges,  the  index  line  is  then  adjusted  so  as  to  coincide 
with  the  zero  of  the  graduated  circle. 

We  now  have  two  sides  of  an  equilateral  triangle  under  conditions 
such  that  they  can  be  moved  parallel  to  their  original  position,  varying 
them  at  will  for  the  width  of  the  space  at  the  beam  of  the  micrometer 
to  represent  the  correct  width  of  flat,  and  gauging,  within  a  limit  of 
Tov&inr  °f  an  mcn?  the  amount  to  be  ground  off  the  point  of  the  tool 
for  any  United  States  Standard  pitch  of  thread. 

We  thus  establish  a  starting-point  at  one-quarter  inch,  and  by 
moving  the  jaws  towards  each  other,  never  necessarily  touching  the 
fine  edges  of  the  jaws, —  for  the  flat  of  any  diameter  of  screw,  however 


165 

small,  must  have  some  appreciable  width, —  an  accurate  adjustable 
gauge  is  available  to  measure  within  the  closest  possible  practical  limit 
the  proper  width  of  flat  as  well  as  the  angle  of  the  tools  used  to  cut  the 
entire  range  of  United  States  Standard  pitches.  This  limit  is  one  so 
close  that  if  the  space  cut  by  any  one  of  these  tools  be  applied  to  the 
thread  produced  by  the  operation,  the  coincidence  is  so  complete  that 
the  light  is  shut  out  at  the  top,  bottom,  and  sides  of  the  thread. 

This  may  be  safely  considered  as  exact  as  machined  work  can  be 
produced  at  the  present  time,  and  certainly  within  limits  which  are 
practicable. 

The  third  point  to  be  covered  —  that  of  producing  an  accurate  lead 
of  the  thread,  the  number  of  threads  per  inch  being  determined  by 
the  Sellers  formula  —  was  obtained  by  the  use  of  a  standard  leading 
screw,  carefully  cut  and  tested,  so  that  it  is  now  entirely  possible  and 
practicable  to  originate  thread  gauges,  applying  the  principles  of  a 
standard  system  of  measurement  such  as  has  been  previously  described, 
and,  having  every  step  known  to  be  within  the  limits  of  accuracy 
necessary,  the  various  operations  described  for  the  production  of 
thread  gauges  become  comparatively  simple,  and  the  results  are  con- 
clusive evidence  that  this  accuracy  has  been  attained. 


From  what  has  already  been  stated,  it  is  evident  that  in  order 
to  produce  gauges  which  shall  accurately  represent  the  United 
States  Standard  or  Franklin  Institute  thread,  the  following  con- 
ditions must  be  secured  in  the  various  stages  of  their  manufac- 
ture, each  condition  being  important  in  its  relation  to  each  of 
the  others,  as  shown  in  the  test  which  is  applied  when  the  gauges 
are  finished,  to  which  reference  has  been  made  and  which  is 
described  later  on ;  a  variation  from  the  limit  of  accuracy  re- 
quired, even  in  only  one  particular,  making  it  impossible  to  meet 
the  requirements  imposed  by  this  test. 

The  points  to  be  considered  are  six  in  number : 

1.  Correct  outside  diameter. 

2.  Correct  diameter  at  the  bottom  or  root  of  the  thread. 

3.  Correct  lead  or  pitch  of  the  thread. 

4.  Correct  angle  (60  degrees)  of  the  thread  in  the  plane  of 
the  axis. 

5.  Correct  position  of  the  tool  in  cutting,  which  must  be  exactly 
at  right  angles  to  the  axis  of  the  gauge. 


166 

6.  Correct  width  of  the  flat  of  the  thread,  top  and  bottom  (one- 
eighth  of  the  pitch). 

The  test  above  referred  to  is  that  of  applying  to  the  thread  of  the 
finished  gauge,  at  the  top  and  sides,  a  thin  templet  of  sheet  steel 
which  has  been  formed  by  the  same  tool  used  to  cut  the  thread 
of  the  gauge,  the  thin  templet  having  been  planed  between  two 
blocks  of  cast  iron  for  the  purpose  of  preserving  the  edges  intact. 

This  templet  or  impression,  being  an  exact  copy  of  the  thread 
space,  together  with  the  width  of  the  bottom  flat,  should  agree 
perfectly  with  the  top  and  sides  of  the  thread  proper  of  the  gana'e. 
Any  variation  which  may  appear,  will  evidently  be  double  the 
amount  which  actually  exists,  owing  to  the  peculiar  conditions 
presented  by  this  form  of  thread. 

.  To  explain  more  fully,  it  might  be  well  to  draw  attention  to  the 
fact  that,  while  the  outside  diameter  may  be  correct,  the  diameter 
at  the  bottom  or  root  of  the  thread  may  not  be  so;  hence  the  width 
of  the  flat  at  the  top  of  the  thread  resulting  from  these  conditions 
will  be  greater  than  one-eighth  of  the  pitch,  providing,  of  course, 
that  the  tool  has  the  proper  width  at  the  edge  or  point  in  cutting 
the  thread.  Reversing  the  conditions,  the  opposite  will  be  the 
result.  Or,  if  the  width  of  the  flat  is  not  one-eighth  of  the  pitch, 
the  diameters  being  both  correct  in  this  case,  the  error  in  the  test 
is  made  doubly  apparent  as  in  the  other  cases  noted  above,  for  in 
applying  the  templet  the  amount  taken  from  one  is  evidently 
added  to  the  other,  hence  the  real  error  is  increased  twice  the 
amount,  making  the  test  a  decisive  one. 

If  the  angle  is  not  sixty  degrees,  or  if  the  cutting  tool  has  not 
been  placed  at  right  angles  to  the  axis  of  the  gauge,  this  error  is 
also  doubled  in  the  test  thus  made;  therefore,  if  at  the  end  of  all 
the  different  operations  required  for  the  production  of  standard 
gauges  for  this  form  of  thread,  this  simple  test  be  found  to  be 
successfully  met,  the  real  error  will  certainly  be  within  a  limit 
necessary  for  interchangeable  gauge  work.  In  other  words,  the 
impression  taken  of  the  bottom  and  sides  of  the  thread  being  an 
exact  copy  of  the  thread  space,  the  actual  variation  is  doubled,  so 
that  if  each  be  incorrect  ^iroiro  of  an  inch,  this  apparent  error 
will  be  indicated  by  a  difference  of  TITOOU  of  an  inch,  which  is 
plainly  perceptible  to  the  eye,  by  the  use  of  the  inspection 
templet  mentioned. 


167 

The  requirements  of  this  test  determine  the  correctness  of 
every  one  of  the  six  conditions  referred  to,  and  even  the  wear 
of  the  threading  tool  itself  has  to  be  allowed  for  in  the  operation 
of  cutting,  in  order  that  the  width  of  the  flat  at  the  point  may 
be  within  the  necessary  limit  at  the  final  moment  to  make  it 
possible  to  meet  this  test  successfully;  so  that  some  idea  may 
be  formed  of  the  care  which  was  necessary  in  all  the  operations 
carried  through  to  produce  the  model  set  of  unhardened  steel 
thread-gauges  made  for  final  reference  by  The  Pratt  &  Whitney 
Company,  in  order  that  every  set  of  gauges  made  thereafter 
might  be  not  only  duplicates,  but  standard  in  every  respect 
within  the  closest  possible  limit. 

In  order  to  definitely  fix  the  proper  number  of  threads  per 
inch  for  any  required  diameter  of  screw  or  bolt,  Mr.  William 
Sellers  constructed  the  following  empirical  formula,  which  serves 
to  determine  independently  of  tables  or  other  aids,  the  correct 
pitches  for  any  diameter  of  bolt,  and  is 


in  which  d  =  the  number  of  sixteenths  in  the  diameter  of  the 
bolt  +  10;  a  =  2.909;  c  =  16.64;  and  p=  pitch  of  the  thread. 

A  simpler  and  more  convenient  form  of  this  equation,  and  one 
which  is  readily  deduced  from  it,  is 

^  =  0.241/^+0.625-0.175,  (a) 

in  which  D  represents  the  diameter  of  the   bolt  or  screw  in 
inches. 

Quoting  exactly  from  the  "  Report  of  the  Board  to  Recom- 
mend A  Standard  Gauge  for  Bolts,  Nuts,  and  Screw  Threads  for 
the  United  States  Navy,"  May,  1868  : 

"  To  illustrate  the  use  of  this  formula,  we  take,  for  example,  a  two- 
inch  bolt  and  let  it  be  required  to  determine  the  pitch  of  the  thread, 
and  the  number  of  threads  per  inch.  Making  the  proper  substitution, 
the  formula  becomes 

ff  =  0.24^2  +  0.  625  —  0.175 
=  0.24^/2.625-0.175 
=  0.24x1.62-0.175 
=  0.2138  of  an  inch. 

"The  reciprocal  of  this,  or  ^1^—4.68,  gives  the  proper  number 
of  threads  per  inch. 

u  For  the  purpose  of  avoiding  the  use  of  troublesome  fractions,  the 
nearest  convenient  aliquot,  or  4£,  is  taken.  This  will  be  found  to  cor- 
respond with  the  number  of  threads  given  in  the  table." 


168 


This  latter  provision  is  designed  to  avoid  the  necessity  for  com- 
plicated screw  cutting  gear,  by  preventing,  as  far  as  possible,  the 
use  of  fractional  threads. 

The  proper  number  of  threads  per  inch  for  all  sizes  of  bolts  or 
screws,  from  one-quarter  to  six  inches,  inclusive,  varying  by  six- 
teenths of  an  inch,  as  found  by  the  application  of  the  foregoing 
formula,  is  given  complete  in  the  table  appended : 


DIAMETER 
OF 
SCREW. 

THREADS 
PER 
INCH. 

DIAMETER 
OF 
SCREW. 

THREADS 
PER 
INCH. 

DIAMETER 
OF 
SCREW. 

THREADS 
PER 
INCH. 

lin.  . 

20 

2A  in. 

4A 

44  in 

21 

A  in 

18 

21  in 

41 

4  ^  in 

2i 

4  in    . 

16 

35  in 

4 

*T¥  1JJ> 

41  in 

21 

-TTf  in 

14 

24  in    . 

4 

4  ^  n 

24 

&  in 

18 

2TV  in 

4. 

71  1  ff  "  • 
44  in 

24 

T9F  in- 
4  in    . 

12 
11 

^Tff  A"' 

2i  in  

2A-  in 

4 
4 

4TV  in. 
4|  in 

2f 
24 

44  in 

10 

24  in. 

4 

4T97r  in 

24 

16 

4  in.  . 

10 

2Uin 

4 

44  in 

24 

44  in 

9 

24  in 

4 

444  in 

24 

16 
l  m. 

9 

244  in 

'Sir 

4f  in 

24 

ft  in. 

g 

.        ~16   "*• 

21  in.  . 

3i 

444  in 

24 

^  iu. 
1    m  

8 

244  in. 

3.1 

.       ^TT  1U- 

4it  in.  . 

24 

IT*  in- 

7 

3    in  

34- 

444  in. 

2i 

Hin   . 

7 

3TSr  in 

31 

^y^    i», 

5    in 

24- 

1A  in 

7 

34  in   . 

3i 

5TV  in 

24- 

ATfr  1U- 

11  in.  . 

7 

3A  in. 

sl 

54  in.  . 

2i 

1A  in 

6 

31  in 

31 

5A  in 

24- 

If  in 

6 

35  in 

8l 

51  in 

21 

1A  in 

6 

34  in.  . 

8 

5A  in- 

2i 

14-  in 

6 

37   in 

3! 

5|in 

24 

1A  in 

54- 

31  in 

3i 

5TV  in 

21 

14  in   . 

54 

3A  in 

8 

51  in  

2| 

144  in 

51 

3|  in  

31 

5  A  in. 

2| 

If  in 

5 

344  in 

3 

5f  in 

24 

144  in 

5 

3fin. 

3 

5H  in 

2£ 

11  in   . 

5 

3J4  in 

3 

5£  in.  . 

2| 

144  in. 

5 

31  in; 

3 

5f|  in. 

21 

2   in 

44- 

344  in 

3 

&j  in   

21 

2A  in 

4! 

Ojy   111. 

4    in 

3 

5fl  in. 

21 

2i  in 

44- 

4A-  in 

24  • 

6    in 

21 

^T¥  1U< 

[Bolts  and  screws  }-J,  jf ,  and  f|  inch  diameter  have  been,  and 
are  now  often  made,  having  11,  10,  and  9  threads  per  inch 
respectively,  and  called  United  States  Standard,  but  under  the 
formula  the  correct  number  of  threads  per  inch  is  as  given  in 
the  table.] 

The  formula  from  which  is  derived  the  correct  diameter  of 
United  States  Standard  bolts  at  the  bottom  of  the  thread,  or 


169 


what  would  be  the  exact  diameter  of  the  "  tap  drill ",  with  no 
allowance  for  clearance,*  is  as  follows : 

d  =  v__          1.2990381          _ 

No.  of  threads  per  inch 

In  which  d  =  the  diameter  at  the  root  of  the  thread,  and  D 
the  diameter  of  the  outside  of  the  thread  of  bolt  or  screw. 

The  width  of  flat  for  any  number  of  threads  per  inch  is 
one-eighth  the  pitch,  or 

W=-( 1 \    (c} 

8  \No.  of  threads  per  inch/     v  ' 

A  table  giving  the  root  or  bottom  diameters  and  widths  of 
flat  for  each  diameter  of  bolt  from  £  to  6  inches  inclusive,  in  sizes 
ordinarily  used,  is  here  appended  : 


DIAMETER. 

NUMBER  THREADS 

DIAMETER  AT 

WIDTH   OF   FLAT, 

INCH. 

PER  INCH. 

ROOT  OF   THREAD. 

TOP  AND  BOTTOM. 

* 

20 

0.1850 

0.0063 

T\ 

18 

0.2403 

0.0069 

16 

0.2938 

0.0078 

& 

14 

0.3447 

0.0089 

1 

I'd 

0.4001 

0.0096 

T90 

12 

0.4542 

0.0104 

{ 

11 

0.5069 

0.0114 

t 

10 

0  6201 

0.0125 

9 

0.7307 

0.0139 

1 

8 

0.8376 

0.0156 

H 

7 

0.9394 

0.0179 

i± 

7 

1.0644 

0.0179 

if 

6 

1.1585 

0.0208 

4 

6 

1.2835 

0.0208 

H 

5| 

1.3888 

0.0227 

if 

5 

1.4902 

0.0250 

i* 

5 

1.6152 

0.0250 

2 

4| 

1.7113 

0.0278 

2i 

4i 

1.9613 

0.0278 

2i 

4 

2.1752 

0.0313 

2£ 

4 

2.4252 

0.0313 

3 

3| 

2.6288 

0.0357 

3i 

8| 

2.8788 

0.0357 

3i 

3± 

3.1003 

0.0385 

8* 

3 

3.3170 

0.0417 

4 

3 

3.5670 

0.0417 

4i 

3i 

3.7982 

0.0435 

4i 

2| 

4.0276 

0.0455 

4f 

2f 

4.2551 

0.0476 

5 

2i 

4.4804 

0.0500 

5i 

2| 

4.7304 

0.0500 

5i 

2| 

4.9530 

0.0526 

5f 

2| 

5.2030 

0.0526 

6 

2i 

5.4226 

0.0556 

•  [The  usual  allowance  above  exact  bottom  diameter  is  from  0.004  for  i  in.,  to  0.010  for  2  in.  taps.] 


170 

A  modification  of  formula  (a),  which  has  met  with  general 
acceptance,  changing  the  coefficient  from  0.24  to  0.23,  or 


p  =  0.23  V ' D  +  0.625  —  0.175,     (d) 

as  proposed  by  the  writer  in  1882,  makes  it  applicable  to  screw 
threads  which  are  smaller  in  diameter  than  one-quarter  of  an 
inch,  and  increases  the  number  of  threads  per  inch  more  rapidly 
as  the  diameter  decreases  than  is  found  to  result  from  the  use  of 
the  original  formula  (a). 

This  formula  might  be  applied  to  the  pitches  of  small  screws 
when  finer  threads  are  desirable,  and  with  the  Sellers  or  United 
States  form  of  thread  it  gives  for  sizes  below  one-quarter  of  an 
inch  a  good  ratio  of  diameter  to  the  pitch,  as  will  be  seen  by 
reference  to  the  following  table : 


1 

DIAMETER. 
INCH. 

NUMBER  OF 
THREADS 

DIAMETER 
AT 

WIDTH 
OF  FLAT, 

PER  INCH. 

ROOT   OF  THREAD. 

TOP   AND   BOTTOM. 

f 

64 

50 

0.0422 

0.0678 

0.0020 

0.0026 

i 

40 

0.0925 

0.0031 

36 

0.1202 

0.0035 

A 

32 

0.1469 

0.0039 

A 

28 

0.1724 

0.0045 

171 


F  The  following  table  of  Briggs  Standard  Pipe  Thread  sizes  is 
taken  from  the  report  of  the  Committee  on  Standard  Pipe  and 
Pipe  Threads,  American  Society  Mechanical  Engineers,  Yol. 
VIII,  Proceedings  of  the  New  York  Meeting,  November  29  to 
December  3,  1886. 

STANDARD  DIMENSIONS  OF  WKOUGHT-!EON  WELDED  TUBES. 


DIAMETER   OP   TUBE. 

SCREWED   ENDS. 

Nominal 
Inside. 

Actual  Inside. 

Actual  Outside. 

THICKNESS 
OF   MH.TAL. 

Number  of 
Threads 
per  Inch. 

Length  of 
Perfect  Screw. 

Inches. 

Inches. 

Inches. 

Inch. 

No. 

Inch. 

i 

0.270 

0.405 

0.068 

27 

0.19 

0.364 

0.540 

0.088 

18 

0.29 

i 

0.494 

0.675 

0.091 

18 

0.30 

i 

0.623 

0.840 

0.109 

14 

0.39 

i 

0.824 

1.050 

0.113 

14 

0.40 

i 

1.048 

1.315 

0.134 

1H 

0.51 

i± 

1.380 

1.660 

0.140 

11* 

0.54 

H 

1.610 

1.900 

0.145 

1H 

0.55 

2 

2.067 

2.375 

0.154 

Hi 

0.58 

2* 

2.468 

2.875 

0.204 

8 

0.89 

3 

3.067 

3.500 

0.217 

8 

0.95 

a* 

3.548 

4.000 

0.226 

8 

1.00 

4 

4.026 

4.500 

0.237 

8 

1.05 

4* 

4.508 

5.000 

0.246 

8 

1.10 

5 

5.045 

5.563 

0.259 

8 

1.16 

6 

6.065 

6.625 

0.280 

8 

1.26 

7 

7.023 

7.625 

0.301 

8 

1.36 

8 

7.982 

8.625 

0.322 

8 

1.46 

9 

9.000 

9.688 

0.344 

8 

1.57 

10 

10.019 

10.750 

0.366 

8 

1.68 

Taper  of  conical  tube  ends,  1  in  32  to  axis  of  tube, 
(f  inch  per  foot  taper  in  diameter.) 

The  length  of  thread  complete,  which  is  represented  by 
standard  pipe  thread-gauges  made  for  this  purpose,  is  determined 
by  adding  to  the  figures  in  the  last  column  the  length  of  two 
threads  for  each  pitch  of  thread,  as  for  instance,  in  the  case  of 
8  threads  per  inch,  the  length  of  a  2|  inch  gauge  would  be  0.89 
+  0.25,  or  1.14;  or,  more  strictly  stating  it,  1.138  inches. 


172 

In  conclusion,  it  might  not  be  out  of  place  to  mention  here  one 
of  the  latest  important  standards  adopted  by  the  American  Rail- 
way Master  Mechanics'  Association,  which  is  designed  to  bring 
about  uniformity  in  the  diameter  of  driving  wheel  centers  and 
tires  for  locomotives,  by  reducing  the  number  of  sizes  to  six  and 
requiring  that  these  be  of  definite  and  standard  diameter. 

The  amount  of  allowance  for  shrinkage  for  each  diameter  of 
wheel  center,  or  the  amount  less  than  the  actual  diameter  of  each 
size  wheel  center,  to  which  tires  must  be  bored,  in  order  to  en- 
sure the  proper  degree  of  strain  within  the  elastic  limit  when  the 
tire  is  "set,"  has  also  been  definitely  established,  so  that  it  is  now 
possible  and  practicable  to  keep  locomotive  tires  ready  bored  in 
stock,  thus  materially  reducing  both  first  cost  and  the  time  re- 
quired for  renewals  or  repairs. 

As  stated  in  the  circular  issued  by  the  Association,  dated  Sep- 
tember 15,  1886,  this  standard  was  unanimously  adopted  at  their 
meeting  held  in  Boston,  June,  1886. 

The  diameters  of  driving  wheel   centers  as  proposed  by  the 
Committee  and  adopted  at  that  time  are  as  follows: 
38  in.,  44  in.,  50  in.,  56  in.,  62  in.,  and  66  in. 

Gauges  representing  these  sizes,  and  also  those  representing 
the  diameter  of  tire  with  shrinkage  allowance  for  each,  have  been 
made  by  The  Pratt  &  Whitney  Company  under  arrangement  with 
the  Committee,  as  stated  in  the  circular,  and  are  for  reference 
only,  the  gauges  for  wheel  centers  being  end-measure  standards 
made  of  weldless  cold  drawn  steel  tube,  with  hardened  steel  ends 
ground  to  standard  size,  and  hence  are  called  "  reference  stand- 
ards "  for  the  diameters  of  wheel  centers  adopted  by  the  Associa- 
tion. The  gauges  for  the  diameter  of  tire  are  calipers  or  "  snap  " 
gauges,  with  hardened  jaws,  and  are  made  entirely  of  tool  steel. 
Each  of  the  latter  gauges  represents  the  diameter  of  a  tire  bored 
to  standard  size  having  the  proper  shrinkage  allowance  as  given 
in  the  table  appended,  which  is  taken  from  the  circular  referred  to : 

38  in.  less  0.040  in., 37.960  in. 


44 
50 
56 
62 
66 


0.047  "  43.953 

0.053  "  49.947 

0.060  "  55.940 

0.066  "  61.934 

0.070  "  .     ..65.930 


ADDENDA. 


At  a  general  meeting  of  the  Society  of  German  Engineers,  held 
in  Leipzig,  August  15, 16,  and  17, 1887,  the  report  of  the  Karls- 
ruhe District  Society,  recommending  a  metric  screw  thread  sys- 
tem, was  submitted,  in  which  was  proposed  for  adoption  a  thread 
having  the  Sellers  form  for  top  and  bottom  of  the  thread,  or  flat 
one-eighth  of  the  pitch,  but  recommending  for  the  angle  of  the 
thread  53°  8',  instead  of  60  degrees,  the  angle  proposed  by  Mr. 
Sellers  and  recommended  by  the  Franklin  Institute. 

A  commission  is  to  be  appointed  to  test  the  practicability  of 
the  system  advocated  by  the  Karlsruhe  Society,  with  a  view  to 
its  general  introduction  throughout  Germany. 


THE   JOHN    SCOTT   LEGACY   MEDAL. 
(Engraving  one-half  size.) 


GENERAL  INDEX. 


Airy,  Sir  George :  Page. 

Formula  for  neutralizing  effect  of  flexure,      .         .         .         .  6,  119 

Baily,  Sir  Francis : 

Baily's  metal,  composition  of,' 117 

Chancy,  H.  J.,  Warden  of  British  Standards, 2,  120 

Chanute,  O.  : 

Investigations  relating  to  size  of  round  iron  for  U.  S.  Standard 

bolts 64 

Investigations  in  relation  to  screw  threads,     ....  65,  72 

Paper  by,  "Uniformity  in  Railway  Rolling  Stock,"        .         .  141 

Coefficient  of  Expansion : 

Determination  of,  by  means  of  ice  water,        .         .         .         .  18 

Example  of  ratio  for  different  materials,         .         .         .         .  13 

General  law  as  to  rate  of  change, 14 

No  correction  necessary  in  use  of  steel  standard  P.  &  W.5,  57 

Table  of  results  in  determination  of  meters  used, ...  20 

Comparator : 

Description  of,        .         .         .         .         .         .         .         .         .  5,  131 

Method  of  testing  accuracy  of, 135 

Rogers-Bond  Universal,  description  of,  .         ...         .         .50,  130 

Saxton's  Reflecting, 126,  129 

Curvature : 

Errors  of, 53 

Correction  of,          ... 135 

Engineering,  London : 

Article  reprinted  from,  on  standard  screw  threads,          .         .  93 

Flexure : 

Determination  of,  using  mercury  surface,        ....  7 

Formula  for  neutralizing,        .......  6 

Forney,  M.  K : 

Chairman  Committee, 77 

Report,  extract  from, 148 

Franklin  Institute : 

Or  United  States  Standard  thread, 144 

Special  committee  report, 78 

Froment,  M. : 

Steel  end-measure  meter,  record  of, 4 


176 

Gauges:  Page 

Briggs  Standard,  pipe  thread, 160 

Briggs  Standard,  table  of  dimensions,  £  to  10  inches,     .         .  171 

Drop-forged  caliper, 157 

Illustrations  of  "  good  and  bad  fit, " 71,155 

Limit,  adoption  by  Master  Car-Builders'  Association,     .         .  91 

Limit  for  round  iron  for  United  States  Standard  bolts,  .         .  88 

Standard  cylindrical  size, 86,  155 

Test  of  end-measure, 55,  142 

Thread,  "  hardened  and  not  ground," 75,87 

Thread,  method  of  making, 73 

Thread,  method  of  grinding  hardened,           ....  75 

Wire  standard, 158 

German  Engineers,  Society  of : 

Form  of  thread  recommended  by  Karlsruhe  Society,  Leipzig 

meeting,  1887, 173 

Letter  to  Franklin  Institute, 92 

Herschell,  Sir  John : 

Uniformity  of  manufactured  articles  compared,      .         .         .  139 

Huyghens : 

Principle  of  vibrations  of  pendulum,     .         .         .         .         .  112 

Imperial  Yard : 

Act  legalizing, 115 

Destruction  of, 116 

Restoration  of, 117 

Where  kept, 120 

Interchangeability : 

Application  of,       .........  159 

International  Bureau  of  Weights  and  Measures,        ....  3 

Kater,  Captain: 

Position  of  neutral  plane  in  standard  bars,     .         .         .         .  118 

Yard  of  the  Royal  Society,     .         .                 .         .         ...  117 

Master  Car-Builders'  Association : 

Committee  report,  .........  59 

Recommendation  of  the  United  States  Standard  or  Franklin 

Institute  thread, 63 

Reference  set  standard  thread  gauges  and  24-inch  line  and 

end-measure  bar,      .* 77 

Master  Mechanics'  Association : 

Recommendation  of  United  States  Standard  thread,       .         .  63 

Reference  set  standard  thread  gauges, 76 

Wire  gauge,  adoption  of  micrometer  as  a  standard  for  reference,  158 

Wheel  center  and  tire  standards  and  gauges,           .         .         .  172 

Molecule : 

Diameter  of, 124 


177 

Measuring  Machine :  Page. 

Description  of  calipering  attachment,  Universal  Comparator,  53 

Improved  12-inch  bench  caliper,     ......  152 

Whitworth,    ....                  .                  ...  151 

Microscope : 

Error  of  focal  distance,            .         .          .         .         .         .         .  17 

Limit  of  error  in  setting  eye-piece  micrometer,       ...  55 

Magnifying  power,          .         .         .         .                   .         .         .  54 

Personal  error  in  reading,       .......  57 

Micrometer : 

For  measuring  flat  of  United  States  Standard  thread  tools,    .  146 

For  wire  gauge  standard,        .......  158 

Pendulum : 

Use  as  a  unit  of  length,           .         .         .          .         .         .         .  112 

Leslie's, .       .         .         .         .  114 

Pennsylvania  Railroad : 

Adoption  of  the  Franklin  Institute  thread  in  1869,         .         .  98 

Railroad  Gazette: 

Article  "A  Screw  Thread  Primer," 83 

Editorial,  September  24,  1886, 106 

Report : 

American  Society  Mechanical  Engineers,  committee    of,    on 

standards  and  gauges, 50 

to  Chief  of  Bureau  of  Steam  Engineering,  extracts  from,       .  62,  167 
Franklin  Institute,  special  committee  on  screw  threads,           .  78 
Hilgard,  Prof.  J.  E.,  United  States  Coast  and  Geodetic  Sur- 
vey,            24 

Master  Car-Builders'  Association,  committee  on  screw  threads,  59 

Rogers,  Prof.  W.  A.,  to  The  Pratt  &  Whitney  Co.,         .  1 

Waldo,  Dr.  Leonard,  on  thermometer  used  by  the  P.  &  W.  Co. ,  49 

Sellers  or  Franklin  Institute  thread, 144 

Sellers,  William: 

Reasons  stated  for  variation  in  original  thread  gauges,   .         .  66 

Screw  Thread : 

Sharp  "V,"  Sellers  or  United  States  Standard,  and  Whitworth,  60 

Primer,  from  Railroad  Gazette,        .         .         .         .         .         .  83 

Sheepshanks,  Rev.  R. : 

In  charge  of  restoration  of  imperial  standards,       .         .         .  117 

Work  legalized  by  Parliament,        ......  120 

Standards : 

Baily's  metal, 117,  125 

Bird's  "  Standard  Yard  1760,"        ...                            .  115 
Bronze  No.  11: 

Comparisons  at  Washington,         .         .         .         .         .  10 

Direct  standard  of  reference, 1 

12 


178 

Standards,  Bronze  No.  11  (continued)  :  page. 

Investigations  in  relation  to  imperial  yard,  ...  2 

Presented  to  the  United  States, 120 

Standard  at  61°.  79  Fahr., 2 

Coast  Survey  yard  and  meter, 19 

Comparisons  by  Drs.  Chaney  and  Benoit,     ...  28 

Comparisons  by  Prof.  W.  A.  Rogers,   .          .         .         .  30 

Construction  of, 8 

Description  of  bars  made  for  the  P.  &  W.  Co.,      ...  5 

Description  of  line-measure  bar  P.  &  W.5,     ....  43,  154 
End-measure  grinding,  .......       9,  56,  142 

End-measure  pieces,  test  of, 55,  142 

Different  values  for  length  of  the  foot,  .         .         .         .         .         112 

Flexure  of, 2,  6,  119 

Graduation  of  4-inch  line-measure  bar  (P.  &  W.  5),        .         .  70,  154 
Imperial  Yard,  composition  of,  .         .         .         •       1>  69,  117 

Investigation  of : 

Yard  and  meter  P.  &  W.  3, 40 

Line  and  end-measure  yard  and  meter  P.  &  W.4,         .  46 

Steel  line-measure  P.  &  W.  5  (4  inch),  ....  45 

Of  length  and  their  subdivision,  Lecture  I,     .         .         .         .         Ill 

Of  length  as  applied  to  gauge  dimensions,  Lecture  II,    .         .         139 

Materials  available  for, .  125 

Materials  necessary  for  practical  purposes,      .         .         .         .    2,  125 

Methods  of  comparison  on  Universal  Comparator,  .         .  52,  13(5 

Methods  of  subdivision  and  investigation,      ....         137 

Metre  des  Archives,        ....  ...  3 

Meter  of  the. Conservatoire  des  Arts  et  Metiers,       .  .    4,  114 

Metric,  limited  use,  practically,  in  this  country,     ...  3 

P.  &  W.  Co.  bronze  bar,  No.  1,      .  .  24,  118 

P.  &  W.  Co.  bronze  bar,  No.  2,  description  of,       .  .  25 

Relation  of  Imperial  yard  to  P.  &  W.j  and  P.  &  W.2,   .          .  27 

Relation  between  P.  &  W.6  and  ^  yard,  46 

Relation  of  yard  and  meter  at  same  temperature,    . 
Russian  iron  bar,  for  geodetic  surveys,   .         .  125 

Shuckburgh's  scale  (0-36  in.),         .  116 

Stevens  Institute  line  and  end-measure  bars  and    Whitwort  li 

steel  yard  used, .3 

Tresca  copper  meter,       .         .  .    12,  125,  126 

Troughton  82-in.  brass  scale,  .  69,  121 

Value  of  line-measure  for  oriyiimtiity  and  prescrriiKj  ttanda/rd 

sizes,         .'•;••' 56,  5S,   15:5 

Whitworth's  method  of  subdivision  of  the  yard,     .  I  ill 

Yard  of  the  Royal  Society,  construction  of ,    .         .  .         117 


179 

Taps,  U.  S.  Standard  :  Page. 

Endurance  or  life  of, 72,  148 

Exact  "  tap  drill "  size, 169 

Temperature : 

Necessary  precautions  to  be  taken,          .         .         .         .         .  16 

Thermometer : 

Indications  of,         .........  15 

Investigation  of,  in  use  by  the  P.  &  W.  Co.,            ...  49 
Thomson,  Sir  William : 

Graphic  illustration  of  an  infinitesimal  dimension  by,      .          .  124 
Thread  Gauges,  U.  S.  Standard : 

Conditions  necessary  to  secure  accuracy,         .         .         .         .  165 

Method  of  establishing  angle  and  width  of  flat,      .         .          144,  161 

Necessity,  of  reference  to  an  accepted  standard  as  a  basis,        .  72 

Necessity  for  and  practical  use  of,            .....  87 

Tolles,  R.  B. : 

Objective  illumination, 134 

Tresca,  M.  and  G.  : 

Transfer  of  meter  by,      ........  4 

Troughton : 

82-in.  brass  scale,  value  of,  and  legal  authority,      .          .          .  69,  121 
Tyndall,  Dr. : 

Extract  from  lecture,       ........  143 

U.  S.  Standard  Thread: 

Adaptation  to  interchangeability,  ......  147 

Angle  of  the  thread  tool,         ......  74 

Correspondence  relating  to, 92 

from   C.,  B.  &  Q.  R.  R.   Co.,                            .  102 

M.  &  St.  P.  Ry.  Co.,       .        ,.         .  101 

R-I.  &  P.  Ry.  Co.,                     .  101 

D.  L.  &  W.  R.  R.  Co.,  100 

L.  &  N.  R.  R.  Co.,       ....  99 

N.  Y.  C.  &  H.  R.  R.  R.  Co.,        .         .  104 

N.  Y.,  L.  E.  &  W.  R.  R.  Co.,      .  105 

P.  R.  R.  Co., 104 

Society  German  Engineers,  .         .         .  92 

The  Pratt  &  Whitney  Co.,   .         .         .  105 
Wahl,    Dr.    Wm.    H.,    Sec'y    Franklin 

Institute, 99 

Formula  for.bottom  diameter, 169 

Formula  for  number  of  threads  per  inch,        .  167,  170 

Formula  for  width  of  flat,       ...                             .         .  169 

Strength  of,    ........  $2 

Table  of  diameters  at  root  of  thread  and  width  of  flat,  .          .  169 

Table  of  sizes  and  threads  per  inch, 168 

Table  of  sizes  below  ^  in.,      .         .  170 


180 

Unit  of  Length :  Page. 

Leslie's  pendulum,           .         .                  .         .         .         .         .  114 

Metre  des  Archives, .          114,  122 

Seconds  pendulum,         .......          112,  115 

Ten-millionth  of  the  earth's  quadrant, 114 

Wave  of  monochromatic  light, 128 

Watts,  James: 

Difficulties  under  which  his  work  was  accomplished,      .         .  141 

Wheel  Center  and  Tire  gauges,         .  .172 

Whitney,  Eli: 

First  to  introduce  iuterchangeability  in  manufacture  of  arms,  141 

Whitworth,  Sir  Joseph: 

Development  by,  of  system  of  interchangeable  gauges,  .          148,  149 

Measuring  machine, 150,  151 

Method  of  subdivision  of  the  yard,         ....  149 

Steel  yard  bar,        .........  3 

Surface  plates,        ...  143 

Wire  Gauge,  Imperial  Standard,       .         .  158 

Zentmayer,  Joseph  : 

Eye-piece  micrometer,     .         .         .         .         .         .         .         .  134 


to  desk  from  which  borrowed. 

on  the  last  date  stamped  below. 


SENT  ON  ILL 

4  ?.006 

.C.  BERKELEY 


REC'DLD 

JUN22'64-4PM 
NOV    6  1978 

LD2l-100m-U,'49(B7146sl6)476 


M323716 


